Using fuzzy set theory to assess country-of-origin effects on te formation of product attit

安全等级特征量及其计算⽅法编号：SM-ZD-33851安全等级特征量及其计算⽅法Through the process agreement to achieve a unified action policy for different people, so as to coordinate action, reduce blindness, and make the work orderly.编制：____________________审核：____________________批准：____________________本⽂档下载后可任意修改安全等级特征量及其计算⽅法简介：该规程资料适⽤于公司或组织通过合理化地制定计划，达成上下级或不同的⼈员之间形成统⼀的⾏动⽅针，明确执⾏⽬标，⼯作内容，执⾏⽅式，执⾏进度，从⽽使整体计划⽬标统⼀，⾏动协调，过程有条不紊。

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【摘要】指出了⽬前⽤模糊评价法确定系统的安全等级所存在的问题和不⾜之处。

分别运⽤模糊随机变量理论和模糊集理论⽽提出了安全等级模糊随机特征量和安全等级模糊特征量的概念及其计算⽅法。

安全等级特征量及安全等级变量，均为安全等级取值论域上的模糊⼦集，⽽并⾮是⼀个确定的点。

还给出了安全等级的绝对可能性和相对可能性的计算⽅法。

实例表明，笔者所提出的安全等级特征量及可能性的计算⽅法是科学的、合理的。

【关键词】安全等级评价模糊随机特征量模糊特征量可能性Characteristic Quantity of Safety Grade and Its CalculationMethodXu Kaili Chen Baozhi（School of Resource and Civil Engineering, NortheastUniversity)Chen Quan(Center for Accident Investigation and Analysis, StateEconomic and Trade Commission)Abstract Using the method of fuzzy evaluation, existingproblems and shortcomings are pointed out as the time ofsystem safety grade being defined. By using fuzzy randomvariable theory and fuzzy set theory, the concept and itscalculation method of fuzzy random characteristic quantity ofsafety grade are put forward. Both characteristicquantity ofsafety grade and its variable are the value obtained from thefuzzy sub-set of safety grade on domain, and are not adefinite point. Calculation method of absolute and relativepossibility is also given. System safety in future can beevaluated and forecasted in a definite condition by thecalculation method of fuzzy random characteristic quantity ofsafety grade. Examples demonstrate that calculation method ofcharacteristic quantity of safety grade and the possibilitypointed out in this paper are scientific and rational.Key words：Safety grade Evaluation Fuzzy randomcharacteristic quantityFuzzy characteristic quantity Possibility1 系统安全等级的模糊性在评价系统的安全⽔平或等级时，⼈们常⽤“极其安全”、“⼗分安全”、“⼗分危险”和“极其危险”等不确定性的语⾔表达⽅式。

Beginning1. In this paper, we focus on the need for2. This paper proceeds as follow.3. The structure of the paper is as follows.4. In this paper, we shall first briefly introduce fuzzy sets and related concepts5. To begin with we will provide a brief background on theIntroduction1. This will be followed by a description of the fuzzy nature of the problem and a detailed presentation ofhow the required membership functions are defined.2. Details on xx and xx are discussed in later sections.3. In the next section, after a statement of the basic problem, various situations involving possibilityknowledge are investigated: first, an entirely possibility model is proposed; then the cases of a fuzzyservice time with stochastic arrivals and non fuzzy service rule is studied; lastly, fuzzy service rule areconsidered.Review1. This review is followed by an introduction.2. A brief summary of some of the relevant concepts in xxx and xxx is presented in Section 2.3. In the next section, a brief review of the .... is given.4. In the next section, a short review of ... is given with special regard to ...5. Section 2 reviews relevant research related to xx.6. Section 1.1 briefly surveys the motivation for a methodology of action, while 1.2 looks at the difficultiesposed by the complexity of systems and outlines the need for development of possibility methods.Body1. Section 1 defines the notion of robustness, and argues for its importance.2. Section 1 devoted to the basic aspects of the FLC decision making logic.3. Section 2 gives the background of the problem which includes xxx4. Section 2 discusses some problems with and approaches to, natural language understanding.5. Section 2 explains how flexibility which often ... can be expressed in terms of fuzzy time window6. Section 3 discusses the aspects of fuzzy set theory that are used in the ...7. Section 3 describes the system itself in a general way, including the ….. and also discusses how to evaluate systemperformance.8. Section 3 describes a new measure of xx.9. Section 3 demonstrates the use of fuzzy possibility theory in the analysis of xx.10. Section 3 is a fine description of fuzzy formulation of human decision.11. Section 3, is developed to the modeling and processing of fuzzy decision rules12. The main idea of the FLC is described in Section 3 while Section 4 describes the xx strategies.13. Section 3 and 4 show experimental studies for verifying the proposed model.14. Section 4 discusses a previous fuzzy set based approach to cost variance investigation.15. Section 4 gives a specific example of xxx.16. Section 4 is the experimental study to make a fuzzy model of memory process.17. Section 4 contains a discussion of the implication of the results of Section 2 and 3.18. Section 4 applies this fuzzy measure to the analysis of xx and illustrate its use on experimental data.19. Section 5 presents the primary results of the paper: a fuzzy set model ..20. Section 5 contains some conclusions plus some ideas for further work.21. Section 6 illustrates the model with an example.22. Various ways of justification and the reasons for their choice are discussed very briefly in Section 2.23. In Section 2 are presented the block diagram expression of a whole model of human DM system24. In Section 2 we shall list a collection of basic assumptions which a ... scheme must satisfy.25. In Section 2 of this paper, we present representation and uniqueness theorems for the fundamental measurement of fuzzinesswhen the domain of discourse is order dense.26. In Section 3, we describe the preliminary results of an empirical studycurrently in progress to verify the measurement model and to construct membership functions.27. In Section 5 is analyzed the inference process through the two kinds of inference experiments...This Section1. In this section, the characteristics and environment under which MRP is designed are described.2. We will provide in this section basic terminologies and notations which are necessary for theunderstanding of subsequent results.Next Section2. The next section describes the mathematics that goes into the computer implementation of such fuzzylogic statements.3. However, it is cumbersome for this purpose and in practical applications the formulae were rearrangedand simplified as discussed in the next section.4. The three components will be described in the next two section, and an example of xx analysis of acomputer information system will then illustrate their use.5. We can interpret the results of Experiments I and II as in the following sections.6. The next section summarizes the method in a from that is useful for arguments based on xxSummary1. This paper concludes with a discussion of future research consideration in section 5.2. Section 5 summarizes the results of this investigation.3. Section 5 gives the conclusions and future directions of research.4. Section 7 provides a summary and a discussion of some extensions of the paper.5. Finally, conclusions and future work are summarized6. The basic questions posed above are then discussed and conclusions are drawn.7. Section 7 is the conclusion of the paper.Chapter 0. Abstract1. A basic problem in the design of xx is presented by the choice of a xx rate for the measurement ofexperimental variables.2. This paper examines a new measure of xx in xx based on fuzzy mathematics which overcomes thedifficulties found in other xx measures.3. This paper describes a system for the analysis of the xx.4. The method involves the construction of xx from fuzzy relations.5. The procedure is useful in analyzing how groups reach a decision.6. The technique used is to employ a newly developed and versatile xx algorithm.7. The usefulness of xx is also considered.8. A brief methodology used in xx is discussed.9. The analysis is useful in xx and xx problem.10. A model is developed for a xx analysis using fuzzy matrices.11. Algorithms to combine these estimates and produce a xx are presented and justified.12. The use of the method is discussed and an example is given.13. Results of an experimental applications of this xx analysis procedure are given to illustrate the proposed technique.14. This paper analyses problems in15. This paper outlines the functions carried out by ...16. This paper includes an illustration of the ...17. This paper provides an overview and information useful for approaching18. Emphasis is placed on the construction of a criterion function by which the xx in achieving a hierarchical system of objectives are evaluated.19. The main emphasis is placed on the problem of xx20. Our proposed model is verified through experimental study.21. The experimental results reveal interesting examples of fuzzy phases of: xx, xx22. The compatibility of a project in terms of cost, and xx are likewise represented by linguistic variables.23. A didactic example is included to illustrate the computational procedureChapter 1. IntroductionTime1. Over the course of the past 30 years, .. has emerged form intuitive2. Technological revolutions have recently hit the industrial world3. The advent of ... systems for has had a significant impact on the4. The development of ... is explored5. During the past decade, the theory of fuzzy sets has developed in a variety of directions6.The concept of xx was investigated quite intensively in recent years7. There has been a turning point in ... methodology in accordance with the advent of ...8. A major concern in ... today is to continue to improve...9. A xx is a latecomer in the part representation arena.10. At the time of this writing, there is still no standard way of xx11. Although a lot of effort is being spent on improving these weaknesses, the efficient and effective method has yet to be developed.12. The pioneer work can be traced to xx [1965].13. To date, none of the methods developed is perfect and all are far from ready to be used in commercial systems.Objective / Goal / Purpose1. The purpose of the inference engine can be outlined as follows:2. The ultimate goal of the xx system is to allow the non experts to utilize the existing knowledge in the area of manual handling of loads, and to provide intelligent, computer aided instruction for xxx.3. The paper concerns the development of a xx4. The scope of this research lies in5. The main theme of the paper is the application of rule based decision making.6. These objectives are to be met with such thoroughness and confidence as to permit ...7. The objectives of the ... operations study are as follows:8. The primary purpose/consideration/objective of9. The ultimate goal of this concept is to provide10. The main objective of such a ... system is to11. The aim of this paper is to provide methods to construct such probability distribution.。

A fuzzy approach to construction project risk assessmentA.Nieto-Morote a,*,F.Ruz-Vila b,1a Project Engineering Department,Polytechnic University of Cartagena,c/Dr.Fleming,s/n,30202Cartagena,Spain bElectric Engineering Department,Polytechnic University of Cartagena,c/Dr.Fleming,s/n,30202Cartagena,SpainReceived 15July 2009;received in revised form 28January 2010;accepted 2February 2010AbstractThe increasing complexity and dynamism of construction projects have imposed substantialuncertainties and subjectivities in the risk analysis process.Most of the real-world risk analysis problems contain a mixture of quantitative and qualitative data;therefore quan-titative risk assessment techniques are inadequate for prioritizing risks.This article presents a risk assessment methodology based on the Fuzzy Sets Theory,which is an effective tool to deal with subjective judgement,and on the Analytic Hierarchy Process (AHP),which is used to structure a large number of risks.The proposed methodology incorporates knowledge and experience acquired from many experts,since they carry out the risks identification and their structuring,and also the subjective judgements of the parameters which are considered to assess the overall risk factor:risk impact,risk probability and risk discrimination.All of these factors are expressed by qualitative scales which are defined by trapezoidal fuzzy numbers to capture the vagueness in the linguistic variables.The most nota-ble differences with other fuzzy risk assessment methods are the use of an algorithm to handle the inconsistencies in the fuzzy preference relation when pair-wise comparison judgements are necessary,and the use of trapezoidal fuzzy numbers until the defuzzification step.An illustrative example on risk assessment of a rehabilitation project of a building is used to demonstrate the proposed methodology.Ó2010Elsevier Ltd and IPMA.All rights reserved.Keywords:Risk assessment;Linguistics variables;Trapezoidal fuzzy numbers;Risk factor1.IntroductionAccording to Mark et al.(2004),risk is simply the potential for complications and problems with respect to the completion of a project task and the achievement of a project goal.Risk is inherent in all project undertakings,as such it can never be fully eliminated,although can be effectively managed to mitigate the impacts to the achieve-ment of project’s goals.Other definitions of risk are available in the literature such as “the exposure the possibility of economic or financial loss or gain,physical damage or injury,or delay,as a consequence of the uncertainty associated with pursu-ing a particular course of action ”(Perry and Hayes,1985;Chapman and Ward,1997),“the probability of losses in aproject ”(Jaafari,2001;Kartam and Kartam,2001),“the likelihood of a detrimental event occurring to the project ”(Baloi and Price,2003);or “a barrier to success ”(Hertz and Thomas,1994).Although risk has been defined in var-ious ways,some common characteristics can be found (Chia,2006):A risk is a future event that may or may not occur. A risk must also be an uncertain event or condition that,if it occurs,has an effect on,at least,one of the project objectives,such as scope,schedule,cost or quality. The probability of the future event occurring must be greater than 0%but less than 100%.Future events that have a zero or 100%chance of occurrence are not risks. The impact or consequence of the future event must be unexpected or unplanned for.There are many different risk sources in the construction projects and some approaches have been suggested in the literature for classifying them.Some classifications are0263-7863/$36.00Ó2010Elsevier Ltd and IPMA.All rights reserved.doi:10.1016/j.ijproman.2010.02.002*Corresponding author.Tel.:+34968326551.E-mail addresses:Ana.nieto@upct.es (A.Nieto-Morote),Paco.ruz@upct.es (F.Ruz-Vila).1Tel.:+34968325351.International Journal of Project Management 29(2011)220–231focused on the risks nature and their magnitude(Cooper and Champan,1987)or on the risks origin(Edwards and Bowen,1998;Zhou et al.,2008).Other use a hierarchical structure of risks(Tah et al.,1993;Wirba et al.,1996)to classify risks according to their origin and to the location of the risk impact in the project.The increasing size and complexity of the construction projects have added risks to their execution.With the need for improved performance in construction project and increasing contractual obligations,the requirement of an effective risk management approach has never been more necessary.On the subject of risk management process,there have recently been a large number of researchers which have proposed different processes.Some of the most important approaches are:PRAM(Chapman,1997),RAMP(Institu-tion of Civil Engineering,2002),PMBOK(Project Man-agement Institute,2008),RMS(Institute of Risk Management,2002).Almost all of these approaches have a similar framework with differences in the established steps in order to get the risks control.Effective risk management involves a four-phase process:1.Risks identification:The process of determining whichrisks may affect the project and documenting their characteristics.2.Risk assessment:The process of prioritizing risks for fur-ther analysis by assessing and combining,generally, their probability of occurrence and impact.3.Risk response:The process of developing options andactions to enhance opportunities and to reduce threats to the project objectives.4.Risk monitoring and reviewing:The process of imple-a risk response plan,tracking identified risks,monitoring residual risks,identifying new risks,and evaluating the risk process effectiveness throughout the project.Risk project management is beneficial if it is imple-mented in a systematic manner from planning stage through the project completion.The unsystematic and arbitrary risk management can endanger the success of the project since most of the risks are very dynamic throughout the project lifetime.2.Fuzzy risk assessment procedureThe nature of construction project has imposed,in the risk analysis process,substantial uncertainties and subjec-tivities,which have hampered the applicability of many risk assessment methods,that are used widely in construc-tion projects and require high quality data,such as Fault Tree Analysis(FTA),Event Tree Analysis(ETA),Proba-bility and impact grids,Sensitivity Analysis,Estimation of System Reliability,Failure Mode and Effect Analysis (Ahmed et al.,2007).Recently,many risk assessment approaches have been based on using linguistic assessments instead of numerical ing Fuzzy Sets Theory(Zadeh,1965),data may be defined on vague,linguistic terms such as lowity,serious impact,or high risk.These terms cannot be defined meaningfully with a precise single value,but Fuzzy Sets Theory provides the means by which these terms may be formally defined in mathematical logic.Several research studies on the risk assessment of con-struction projects using fuzzy approaches have been per-formed.Some fuzzy proposals have been inspired in the classical risk assessment methods,such as,ETA and FTA:Fujino(1994)demonstrates the applicability of the proposed fuzzy FTA methodology to some cases of con-struction site accidents in Japan;Huang et al.(2001)pro-poses a fuzzy formal procedure in order to integrate both human-error and hardware failure events into a ETA meth-odology;Cho et al.(2002)proposes a fuzzy ETA method-ology characterized by the use of new forms of fuzzy membership curves.However,the research studies have not only been focused on using fuzzy concepts into conventional risk assessment frameworks,but rather new methods have been proposed.Carr and Tah(2001)define a formal model based on a hierarchical risk breakdown structure.The risks descriptions and their consequences are defined using lin-guistic variables and the relationship between the likeli-hood of occurrence(L),the severity(V)and the effect of a risk factor(E)is represented by rules such as“If L and V then E”.Zeng et al.(2007)propose a risk assessment model based on fuzzy reasoning and AHP approach.A modified analytical hierarchy process is used to structure and prioritize risks considering three fundamental risk parameters:risk likelihood(RL),risk severity(RS)and factor index(FI),defined all of them in terms of linguistic variables which are transformed into trapezoidal fuzzy numbers.The relations between input parameters FI,RL, RS and output named Risk magnitude(RM)are presented in form of“if...then”rules.Dikmen et al.(2007)propose a methodology for risk rating of international construction projects.Once the risks have been identified and modelled using Influence Diagrams,they are assessed by linguistic terms.The relationships between risks and influencing fac-tors are captured from the knowledge of experts by using ‘‘aggregation rules’’,where the risk knowledge is explained in form of“if...then”rules.The aggregation of fuzzy rules into a fuzzy cost overrun risk rating is carried out by fuzzy operations.Wang and Elhag(2007)proposes a risk assessment methodology which allows experts to eval-uate risk factors,in terms of likelihood and consequences, using linguistic terms.Also it is provided two alternative algorithms to aggregate the assessments of multiple risk factors,one of which offers a rapid assessment and the other one leads to an exact assessment.Zhang and Zou (2007)propose a methodology based on a hierarchical structure of risks associated with a construction project. Based on expert judgment,the weight coefficients of riskA.Nieto-Morote,F.Ruz-Vila/International Journal of Project Management29(2011)220–231221groups and risk factors are acquired with the aid of the AHP techniques and the fuzzy evaluation matrixes of risk factors.Then the aggregation of weight coefficients and fuzzy evaluation matrices produces the appraisal vector of risky conditions of the construction project.It can be affirmed that all the proposed fuzzy risk assess-ment methods have a common procedure(Lyons and Skit-more,2004):1.Definition and measurement of parameters:The funda-mental parameters,by which the risks associated witha project are assessed,are risk probability and riskseverity,although other parameters can be defined.The measurement of these parameters frequently is dif-ficult due to the great uncertainty involved.In these cases,the measurement of each parameter is made in vague data or linguistic terms and converted into its cor-responding fuzzy number.2.Definition of fuzzy inference:The relations between inputparameters and output parameters can be defined in form of“if-then”rules or in form of mathematical function defined by an appropriated fuzzy arithmetic operator. 3.Defuzzification:As the result of a fuzzy inference phaseis a fuzzy number,this step is used to convert the fuzzy result into a exact numerical value that can adequately represent it.In some risk assessment methodologies,some judge-ments are done by means of pair-wise comparisons(Zeng et al.,2007;Wang and Elhag,2007;Zhang and Zou, 2007).Preference information of alternatives generally pre-sents inconsistency problems.Although there are a large number of studies about the inconsistency of fuzzy prefer-ence relations(Dong et al.,2008;Ghazanfari and Nojavan, 2004);(Herrera-Viedma et al.,2004;Ma et al.,2006;Wang and Chen,2008),none of the proposed fuzzy risk assess-ment methodologies take into account the inconsistency of the judgements.This paper presents a fuzzy risk assess-ment model which most significant difference with other fuzzy risk assessment methods is the use of an algorithm to handle the inconsistencies in the fuzzy preference rela-tion when pair-wise comparison judgements are necessary.3.Fuzzy Sets TheoryThe Fuzzy Set Theory introduced by Zadeh(1965)is suitable for dealing with imprecision and uncertainty asso-ciated with data in risk assessment problems.In a universal set of discourse X,a fuzzy subset A of X is defined by a membership function l A(x),which maps each element x in X to a real number in the interval[0,1].The function value of l A(x)signifies the grade of membership of x in A.When l A(x)is large,its grade of membership of x in A is strong(Kaufmann and Gupta,1991).Among the various types of fuzzy sets of special signif-icance are fuzzy numbers(Dubois and Prade1978)defined as A={x,l A(x)}where x takes its number on the real line R and membership function l A:R!½0;1 ,which have the following properties:A continuous mapping from R to the closed interval[0,1].Constant on(À1,a]:l A(x)=0"x(À1,a].Strictly increasing on[a,b].Constant on[b,c]:l A(x)=1"x[b,c].Strictly decreasing on[c,d].Constant on[d,1):l A(x)=0"x[d,1).where a,b,c and d are real numbers and eventually a=À1,or b=c,or a=b,or c=d or d=1.For convenience,l LAis named as left membership func-tion of a fuzzy number A,defining l LAðxÞ¼l AðxÞ,for allx½a;b ;l RAis named as right membership function of a fuzzynumber A,defining l RAðxÞ¼l AðxÞ,for all x[c,d].A trapezoidal fuzzy number A is a fuzzy number denoted as A=(a,b,c,d)which membership function is defined as:l AðxÞ¼0for x<al LAðxÞ¼xÀa for a6x6b1for b6x6cl RAðxÞ¼xÀd for c6x6d0for x>d26666664ð1Þwhere a,b,c and d are real numbers and a<b<c<d.If b=c,it is defined a triangular fuzzy number.By the extension principle(Zadeh,1965),the fuzzy arithmetic operations of any two trapezoidal fuzzy num-bers follow these operational laws:Fuzzy addition:A1ÈA2¼ða1þa2;b1þb2;c1þc2;d1þd2Þð2ÞFuzzy subtraction:A1H A2¼ða1Àd2;b1Àc2;c1Àb2;d1Àa2Þð3ÞFuzzy multiplication:A1 A2%ða1Âa2;b1Âb2;c1Âc2;d1Âd2Þð4ÞFuzzy division:A1;A2%ða1=d2;b1=c2;c1=b2;d1=a2Þð5ÞThe fuzzy addition or the fuzzy subtraction of any two fuz-zy trapezoidal numbers is also a trapezoidal fuzzy number. But the fuzzy multiplication or the fuzzy division is only approximate a trapezoidal fuzzy number.The scalar multiplication of a trapezoidal fuzzy number is also a trapezoidal fuzzy number defined as:kÂA¼ðkÂa;kÂb;kÂc;kÂdÞif k>0kÂA¼ðkÂd;kÂc;kÂb;kÂaÞif k<0ð6Þ3.1.The algebraic operations of fuzzy numbers based on a-cut conceptThe a-cuts of a fuzzy number A with membership func-tion l A(x)are defined as the crisp set that contains all the222 A.Nieto-Morote,F.Ruz-Vila/International Journal of Project Management29(2011)220–231elements of R whose membership grades in A are greater or equal to the specified value of a:A a¼f x j l AðxÞP a;0P a P1gð7Þand denoted it by A al ;A arÂÃ,i.e.,A a¼½A al ;A ar.The multiplication and division operations on closedintervals,A a¼A al ;A arÂÃand B a¼B al ;B arÂÃ,are defined as (Klir and Yuan,1995):Multiplication:ðAÂBÞa¼½A al ÂB al;A arÂB arð8ÞDivision:ðAÄBÞa¼½A al =B ar;A ar=B alð9ÞAccording the extension principle(Zadeh,1965),an arbi-trary fuzzy set A can fully and uniquely be represented as: A¼[a2½0;1a A aðxÞð10Þwhere U denotes the standard fuzzy union and a aA denotesthe special fuzzy set which membership function is defined as:la A a ¼a for x2A a0for x R A a&ð11ÞTherefore,the multiplication and division operations of4.Proposed risk assessment modelA risk assessment model,based on fuzzy reasoning,is proposed as shown in Fig.1.The model consists of three steps:preliminary step,definition of risk factor function and measurement of variables step and fuzzy inference step.The details are described in the following sections.4.1.Preliminary step4.1.1.Establish a risk assessment groupThe members in a risk assessment group must be care-fully selected.The selected experts will have a high degree of knowledge and previous experience in similar construc-tion projects.The risk assessment team must include the following experts:project managers,project team mem-bers,customers,subject matter experts from outside the project team,end users,stakeholders and risk management group.The members in the risk assessment group will under-take the risk identification,even though all project person-nel should be encouraged to identify risks.Also,the risk assessment group will undertake the measure of risk func-tion parameters.A.Nieto-Morote,F.Ruz-Vila/International Journal of Project Management29(2011)220–231223The risks identification is an iterative process because the risks may evolve or new risks become known as the project progresses through its life cycle.The iteration fre-quency and who participate in each cycle will depend on the characteristics of the project.The experts in a risk assessment group have intuitive methods of recognizing a risk situation.Anyway,there are some risks identification tools as:Checklist,Influence Diagrams,Cause and Effect Diagrams,Failure Mode and Effect Analysis,Hazard and Operability Study,Fault Trees and Event Tree(Ahmed et al.,2007).4.1.3.Construct hierarchical structure of risksThe members in the risk assessment group are required to identify and classify the risks associated with the con-struction project.To decompose the risks into adequate details in which they can be efficiently assessed,a hierarchi-cal structure of risks is generated.The risks are sorted into n groups on the basis of the types of risks,as shown in Fig.2.More levels of decomposition can be incorporated into the hierarchical structure whenever the elements of a given level are mutually independent,but comparable to the elements of the same level.4.2.Definition of risk factor function and measurement of variables step4.2.1.Define risk factor functionThe risk factor(RF)can usually be assessed by consid-ering two fundamental risk parameters:risk impact(RI) and risk probability(RP).The risk impact parameter inves-tigates the potential effect of the risk on a project objective such as schedule,cost,quality or performance.The risk probability parameter investigates the likelihood that each specific risk will occur.These parameters do not take into consideration the impact of the risk to the overall frame-work of the project.In order to assess the risks efficiently and effectively,a parameter,named risk discrimination (RD),is proposed by Cervone(2006).The risk discrimina-tion parameter provides an additional perspective because it gauges the impact of the risk to the overall framework of the project,rather than looking at each risk as an inde-pendent variable within the project.With each risk evalu-ated in the context of the three dimensions,a value can be assigned to each risk using Eq.(14):Overall risk factor¼risk impactÂrisk probabilityrisk discriminationð14Þ4.2.2.Define linguistic scales and associated fuzzy numbersFrequently,it may be extremely difficult to assess the risk associated with a project due to the great uncertainty involved.The imprecision comes from a variety of sources such as,unquantifiable information,incomplete informa-tion or non-obtainable information(Chen and Hwang, 1992).When the members in a risk assessment group have inexact information about risks associated with a project, the assessments cannot be exact but approximate.In these circumstances,the judgements of the members in a risk assessment group are expressed by means of linguistic term instead of real numbers.An important aspect to handle this kind of problems is to define the linguistic terms that will be used.The possible linguistic terms that can be used depends on the nature of the problem.The linguistic terms which generally can be used to assess the parameters of a risk assessment problem, risk impact,risk probability and risk discrimination are the following ones:For evaluating thefirst dimension,RI,afive-point scale is defined:Critical(C),Serious(S),Moderate(Mo), Minor(Mi)and Negligible(N).For the second dimension,RP,a three-point scale is proposed:High(H),Medium(M)and Low probability (L).The third parameter,RD,will be obtained by pair-wise comparison between risks.The selected comparison scale is:Much less(Ml),Less(L),Same(S),More(M) and Much more(Mm).The linguistics terms must be transformed into a fuzzy numbers by using appropriate conversion scale.One of the key points in fuzzy modelling is the definition of fuzzy numbers which represent vague concepts and imprecise terms expressed in a natural language.The representation does not only depend on the concept but also on the context in which it is used.Even for similar contexts,fuzzy numbers representing the same concept may vary considerably.When operating with fuzzy numbers,the result of our calculations strongly depend on the shape of the member-ship functions of these numbers.Less regularmembership Fig.2.Generic hierarchical structure of risks.functions lead to more complicated calculations.More-over,fuzzy numbers with simpler shape of membership functions often have more intuitive and more natural interpretation.All these reasons cause a natural need of simple approx-imations of fuzzy numbers which are easy to handle and have a natural interpretation.For the sake of simplicity the trapezoidal or triangular fuzzy numbers are most com-mon in current applications.As noted in a research study (Mayor and Trillas,1986),the precision in the shape of the membership functions often is not important because of the quantitative nature of the problems with vague pred-icates;thus they are generally written as linearly as possi-ble.Normally it is sufficient to use a trapezoidal representation,as it makes it possible to define them with no more than four parameters.Based on some researches,a numerical approximation system is proposed to systematically convert linguistic terms into their corresponding fuzzy numbers(Chen and Hwang, 1992).The used linguistic terms,their meaning and their associated membership function are shown in Table1. 4.2.3.Define of RI and RP parameters4.2.3.1.Measure RI and RP.The RI and RP parameters of each risk at the bottom level of the hierarchy must be mea-sured by each member in the risk assessment group using the defined linguistic scales.The linguistic measures for RI and RP assigned by each member in the group are con-verted into their corresponding fuzzy numbers according to Table1.The fuzzy numbers obtained for RI and RPparameters are RI mi and RP miwhere i is the number of risksat the bottom level of the hierarchy and m is the number of members in risk assessment group.4.2.3.2.Aggregate individual fuzzy numbers into a groupfuzzy number.The individual fuzzy numbers RI mi and RP mi,corresponding to each one of the m expert in the risk assessment group,are aggregated into group fuzzy number by using the fuzzy arithmetic average,which is defined as:RI i¼1mÂX mn¼1RI ni¼1mÂðRI1iÈRI2iÈÁÁÁÈRI miÞð15ÞRP i¼1mÂX mn¼1RP ni¼1mÂðRP1iÈRP2iÈÁÁÁÈRP miÞð16Þwhere i is each one of the risks at the bottom level of the hierarchy,m is the number of members in risk assessment group,Âis the scalar multiplication defined in Eq.(6) andÈis the fuzzy addition defined in Eq.(2).4.2.4.Measure RD parameterpare risks pair-wise.The members in the risk assessment group are required to provide their comparative judgement on the impact on overall framework of the pro-ject for each risk pair-wise of the same level and group in the hierarchical structure.These linguistic measures are converted into their corre-sponding fuzzy members according to Table1.For each member in risk assessment group it is obtained the follow-ing comparison matrix for the group g and the level l in the hierarchy:A mgl¼r1r2ÁÁÁr nr1r2ÁÁÁr n–ðRDCÞm12ÁÁÁRDC1n mðRDCÞm21–ÁÁÁRDC m2nÁÁÁÁÁÁÁÁÁÁÁÁðRDCÞn1m RDC n2mÁÁÁ–2666666437777775ð17Þwhere n is the number of risks of the group g and the level l in the hierarchy and m is the number of members in risk assessment group.4.2.4.2.Aggregate individual fuzzy numbers into a group fuzzy number.The comparative fuzzy numbers of each one of the members in the risk assessment group are aggregated into a group fuzzy number by using the fuzzy arithmetic average which is defined as:Table1Descriptions of RI,RP and RD comparison.Description of RI General interpretation Fuzzy number Critical(C)Involved very highly impact(0.8,0.9,1,1) Serious(S)Involved highly impact(0.6,0.75,0.75,0.9) Moderate(Mo)Involved moderate impact(0.3,0.5,0.5,0.7) Minor(Mi)Involved only small impact(0.1,0.25,0.25,0.4) Negligible(N)Involved no substantive impact(0,0,0.1,0.2) Description of RP General interpretationHigh(H)Very likely to occur(0.7,0.9,1,1) Medium(M)Likely to occur(0.2,0.5,0.5,0.8) Low(L)Occurrence is unlikely(0,0,0.1,0.2) Description of RDC General interpretationMuch more Much more impact on overall framework of project than(0,0,0,0.3)More More impact on overall framework of project than(0,0.25,0.25,0.5) Same Same impact on overall framework of project than(0.3,0.5,0.5,0.7) Less Less impact on overall framework of project than(0.5,0.75,0.75,1) Much less Much less impact on overall framework of project than(0.7,1,1,1)A.Nieto-Morote,F.Ruz-Vila/International Journal of Project Management29(2011)220–231225RDC ij¼1mÂX mn¼1RDC nij¼1mÂðRDC1ijÈRDC2ijÈÁÁÁÈRDC mijÞð18Þwhere i and j are the risks of the group g and the level l in the hierarchy and m is the number of members in risk assessment group,Âis the scalar multiplication defined in Eq.(6)andÈis the fuzzy addition defined in Eq.(2).The matrix for the group g and the level l in the hierar-chy of comparative fuzzy numbers is defined as:A gl¼r1r2ÁÁÁr nr1r2ÁÁÁr n–ðRDCÞ12ÁÁÁRDC1nðRDCÞ21–ÁÁÁRDC2nÁÁÁÁÁÁÁÁÁÁÁÁðRDCÞn1RDC n2ÁÁÁ–2666666437777775ð19Þwhere n is the number of risks of the group g and the level l in the hierarchy.4.2.4.3.Estimate RD local(RD*).This problem is solved by using fuzzy classical methods of criteria weight calcula-tion adapted to operate with trapezoidal fuzzy numbers.In the fuzzy classical methods,the decision maker(DM) provides its fuzzy preference relations on criteria pair-wise, W ij.The ratio W ij denotes the preference degree of the cri-teria c i over c j and it is usually defined as a fuzzy singleton, which is a fuzzy set which contains only one element.If values of the fuzzy preference relations on criteriapair-wise were consistent,W0ij ,by the reciprocal propertyof fuzzy preference relation,i.e.,W0ij +W0ij=1,therewould be an explicit functional relation between W0ij andthe fuzzy values w i and w j,which would reflect the ranking values of the criteria c i and c j(Ma et al.,2006):W0ij¼0:5½1þwðw iÞÀwðw jÞ ð20Þwhere w(w i)can be any non-decreasing function andP w i=1.By the reciprocal property of preference of the valuesW0ij ,the Eq.(20)satisfies the additive transitivity property,i.e.,W0ik +W0ik+W0ki=1.5In order to keep the simplicity of the method,if w (w i)=w i then Eq.(20)is transformed into a new equation defined as:W0ij ¼w iþð1Àw jÞð21ÞGenerally the pair-wise comparison information given bythe DM has inconsistency,that is W0ik <0.5for W ij P0.5and W jk P0.5.Transitivity is the property that is usually accepted to deal with problems of fuzzy preference relations consistency(Wang and Chen,2008;Dong et al.,2008).Due to the fuzziness of the opinions and the weak tran-sitivity restriction considered,that is,W ik P0.5for W ij P 0.5and W jk P0.5(Herrera-Viedma et al.,2004),an accu-rate solution for this problem could not be found.The w i and w j values are calculated by difference minimization method of the value W ij,obtained directly from the experts, and the value W0ij,defined as a ideal fuzzy preference rela-tions which are consistent:minX ni¼1X nj¼1i¼1ðW0ijÀW ijÞ2264375ð22ÞIn our case,the values of fuzzy preference relations on risks obtained directly from the experts,RDC ij,and the values of the ideal fuzzy preference relations on risks,which areconsistent,RDC0ij,are trapezoidal fuzzy numbers.The extension of this classical method to fuzzy method can be expressed as:minX ni¼1X nj¼1i¼1RDC0ijH RDC ij2264375ð23Þwhere RDC0ijis defined in terms of the fuzzy values of RDÃi and RDÃj,which reflect the ranking values of the risks r i and r j,as:RDC0ij¼RDÃiÈð1H RDÃjÞð24Þwhere i and j are risks of the group g and the level l in the hierarchy andÈand H represents the fuzzy addition and subtraction using Eqs.(2)and(3).The main implication of this method is that the sum ofRDÃishould be now a trapezoidal fuzzy number“around one”that must be defined correctly to get a solution.The matrix for the group g and the level l in the hierar-chy of the RD*fuzzy values are defined as:B gl¼r1r2ÁÁÁr nRDÃ1RDÃ2ÁÁÁRDÁÁÁn2666437775ð25Þwhere n is the number of risks of the group g and the level l in the hierarchy.4.2.4.4.Aggregate RD*in hierarchy.Assume the risk r i has t upper groups at different level in the risk structure hierar-chy and RDÃðjÞgroupis the value RD*of the jth upper group which contain the risk r i in the hierarchy.Thefinal value of RD for each risk r i can be calculated by:RD¼iRDÃiY tj¼1ðRDÃÞðjÞgroupð26Þwhere i is each one of the risks at the bottom level of the hierarchy and represent the fuzzy multiplication using arithmetic operations on their a-cuts in Eq.(12).4.3.Fuzzy inference stepIn the fuzzy inference step,risk analysts convert the aggregated fuzzy number of RI,RP and RD into a fuzzy226 A.Nieto-Morote,F.Ruz-Vila/International Journal of Project Management29(2011)220–231。

I.J. Intelligent Systems and Applications, 2013, 03, 74-82Published Online February 2013 in MECS (/)DOI: 10.5815/ijisa.2013.03.08A Type-2 Fuzzy Logic Based Framework forFunction PointsAnupama KaushikDept. of IT, Maharaja Surajmal Institute of Technology, GGSIP University, Delhi, Indiaanupama@msit.inA.K. SoniDept. of IT, School of Engineering and Technology, Sharda University, Greater Noida, Indiaak.soni@sharda.ac.inRachna SoniDept. of Computer Science and Applications, DAV College, Yamuna Nagar, Haryana, Indiasonirachna67@Abstract —Software effort estimation is very crucial in software project planning. Accurate software estimation is very critical for a project success. There are many software prediction models and all of them utilize software size as a key factor to estimate effort. Function Points size metric is a popular method for estimating and measuring the size of application software based on the functionality of the software from the user‘s point of view. While there is a great advancement in software development, the weight values assigned to count standard FP remains the same. In this paper the concepts of calibrating the function point weights using Type-2 fuzzy logic framework is provided whose aim is to estimate a more accurate software size for various software applications and to improve the effort estimation of software projects. Evaluation experiments have shown the framework to be promising.Index Terms —Project management, Software Effort Estimation, Type-2 Fuzzy Logic System, Function Point AnalysisI.IntroductionSoftware development has become an important activity for many modern organizations. Software engineers have become more and more concerned about accurately predicting the cost and quality of software product under development. Consequently, many models for estimating software cost have been proposed such as Constructive Cost Model(COCOMO) [1],Constructive Cost Model II (COCOMO II) [2], Software Life Cycle Management (SLIM) [3] etc. These models identify key contributors to effort and use historical organizational projects data to generate a set of mathematical formulae that relates these contributors to effort. Such a set of mathematical formulae are often referred to as parametric model because alternative scenarios can be defined by changing the assumed values of a set of fixed coefficients (parameters) [4]. All these models use the software size as the major determinant of effort. Function Points is an ideal software size metric to estimate cost since it can be used in the early development phase, such as requirement, measures the software functional size from user‘s view, and is programming language independent [5].Today the scenario of software industry has changed from what it has many years ago. Now-a-days the object oriented paradigm has incorporated into the software development which leads to the creation of object oriented function points [6]. All the traditional cost estimation models are limited by their inability to cope with vagueness and imprecision in the early stages of the software life cycle. So, a number of soft computing approaches like fuzzy logic (FL), artificial neural networks (ANN), evolutionary computation (EC) etc. are incorporated to make rational decisions in an environment of uncertainty and vagueness. The first realization of the fuzziness of several aspects of COCOMO was that of Fei and Liu [7] called F-COCOMO. Jack Ryder [8] investigated the application of fuzzy modelling techniques to COCOMO and the Function Points models, respectively. Venkatachalam [9] investigated the application of artificial neural network (ANN) to software cost estimation. Many researchers have applied the evolutionary computation approach towards cost estimation [10, 11].1.1 Background and related workOsias de Souza Lima Junior et al. [12] have worked on trapezoidal fuzzy numbers to model function point analysis for the development and enhancement projectassessment. Ho Leung [13] has presented a case study for evaluation of function points. Finnie et al. [14] provided the combination of machine learning approach with FP. They compared the three approaches i.e. regression analysis, artificial neural networks and case based reasoning using FP as an estimate of software size. The authors observed that both artificial neural networks and case based reasoning performed well on the given dataset in contrast to regression analysis. They concluded that case based reasoning is appealing because of its similarity to the expert judgement approach and for its potential in supporting human judgement. Al-Hajri et al. [15] establish a new FP weight system using artificial neural network. Lima et al. [16] proposed the concepts and properties from fuzzy set theory to extend FP analysis into a fuzzy FP analysis and the calibration was done using a small database comprised of legacy systems developed mainly in Natural 2, Microsoft Access and Microsoft Visual Basic. Yau and Tsoi [17] introduced a fuzzified FP analysis model to help software size estimators to express their judgement and use fuzzy B-spline membership function to derive their assessment values. The weak point of their work is that they use limited in-house software to validate the model. Abran and Robillard‘s empirical study [18] demonstrates the clear relationship between FPA‘s primary component and work-effort. Kralj et al. [19] identified the function point analysis method deficiency of upper boundaries in the rating complexity process and proposed an improved FPA method. Wei Xia et al. [20] proposed a Neuro-Fuzzy calibration approach for function point complexity weights. Their model provided an equation between Unadjusted Function Points and work effort which is used to train the neural network and estimated the effort. Moataz A. Ahmed and Zeeshan Muzaffar [4] provided an effort prediction framework that is based on type-2 fuzzy logic to allow handling imprecision and uncertainty present in the effort prediction. Mohd. Sadiq et al. [21] developed two different linear regression models using fuzzy function point and non fuzzy function point in order to predict the software project effort.The above researches have concluded that the combination of soft computing approaches and the traditional cost estimation models yields a more accurate prediction of software costs and effort. All the earlier work on software cost estimation using fuzzy logic incorporated type-1 or type-2 fuzzy framework for effort prediction. This paper proposes an improved FPA method by calibrating the function point‘s weight using type-2 fuzzy logic framework.1.2 Function Point Analysis: A short description Function point analysis is a process used to calculate the software size from the user‘s point of view, i.e. on the basis of what the user requests and receives in return from the system. Allan J Albrecht [22] of IBM proposed Function Point Count (FPC) as a size measure in the late 1970s. Albrecht had taken up the task of arriving at size measures of software systems to compute a productivity measure that could be used across programming languages and development technologies. The current promoter of Albrecht‘s function point model is the International Function Point User‘s Group (IFPUG). IFPUG evolves the FPA method and periodically releases the Counting Practices Manual for consistent counting of function points across different organizations. In FPA, a system is decomposed into five functional units: Internal Logical Files (ILF), External Interface Files (EIF), External Inputs (EI), External Outputs (EO) and External Inquiry (EQ). These functional units are categorized into data functional units and transactional function units. All the functions do not provide the same functionality to the user. Hence, the function points contributed by each function varies depending upon the type of function (ILF, EIF, EI, EO or EQ) and complexity (Simple, Average or Complex) of the function. The data functions complexity is based on the number of Data Element Types (DET) and number of Record Element Types (RET). The transactional functions are classified according to the number of file types referenced (FTRs) and the number of DETs. The complexity matrix for all the five components is given in Table 1, Table 2 and Table 3. Table 4 illustrates how each function component is then assigned a weight according to its complexity.The actual calculation process of FPA is accomplished in three stages: (i) determine the unadjusted function points (UFP); (ii) calculate the value adjustment factor (VAF); (iii) calculate the final adjusted function points.The Unadjusted Function Points (UFP) is calculated using ―(1)‖, where W ij are the complexity weights and Z ij are the counts for each function component.∑∑ (1) The second stage, calculating the value adjustment factor (VAF), is derived from the sum of the degree of influence (DI) of the 14 general system characteristics (GSCs). The DI of each one of these characteristics ranges from 0 to 5 as follows: (i) 0 – no influence; (ii) 1 –incidental influence; (iii) 2 –moderate influence; (iv) 3 – average influence; (v) 4 – significant influence; and (vi) 5 – strong influence.The general characteristics of a system are: (i) data communications; (ii) distributed data processing; (iii) performance; (iv) heavily used configuration; (v) transaction rate; (vi) online data entry; (vii) end-user efficiency; (viii) on-line update; (ix) complex processing; (x) reusability; (xi) installation ease; (xii) operational ease; (xiii) multiple sites; and (xiv) facilitate change. VAF is then computed using ―(2)‖:∑ (2)x i is the Degree of Influence (DI) rating of each GSC. Finally, the adjusted function points are calculated as given in ―(3)‖.(3)Table 1: Complexity Matrix of ILF/EIFTable 2: Complexity Matrix of EITable 3: Complexity Matrix of EO/EQTable 4: Functional Units with weighting factorsII.Type 2 Fuzzy Logic SystemsFuzzy Logic is a methodology to solve problems which are too complex to be understood quantitatively. It is based on fuzzy set theory and introduced in 1965 by Prof. Zadeh in the paper fuzzy sets [23]. It is a theory of classes with unsharp boundaries, and considered as an extension of the classical set theory [24]. The membership µA(x) of an element x of a classical set A, as subset of the universe X, is defined by:µA(x) = {That is, x is a member of set A (µA (x) = 1) or not (µA (x) = 0). The classical sets where the membership value is either zero or one are referred to as crisp sets. Fuzzy sets allow partial membership. A fuzzy set A is defined by giving a reference set X, called the universe and a mapping;µA : X []called the membership function of the fuzzy set A µA(x), for x X is interpreted as the degree of membership of x in the fuzzy set A. A membership function is a curve that defines how each point in the input space is mapped to a membership value between 0 and 1. The higher the membership x has in the fuzzy set A, the more true that x is A. The membership functions (MFs) may be triangular, trapezoidal, Gaussian, parabolic etc.Fuzzy logic allows variables to take on qualitative values which are words. When qualitative values are used, these degrees may be managed by specific inferential procedures. Just as in fuzzy set theory the set membership values can range (inclusively) between 0 and 1, in fuzzy logic the degree of truth of a statement can range between 0 and 1 and is not constrained to the two truth values {true, false} as in classic predicate logic.Fuzzy Logic System (FLS) is the name given to any system that has a direct relationship with fuzzy concepts. The most popular fuzzy logic systems in the literature may be classified into three types [25]: pure fuzzy logic systems, Takagi and Sugeno‘s fuzzy system and fuzzy logic system with fuzzifier and defuzzifier also known as Mamdani system. As most of the engineering applications use crisp data as input and produce crisp data as output, the Mamdani system [26] is the most widely used one where the fuzzifier maps crisp inputs into fuzzy sets and the defuzzifier maps fuzzy sets into crisp outputs.Zadeh [27], proposed more sophisticated kinds of fuzzy sets, called type-2 fuzzy sets (T2FSs). A type-2 fuzzy set lets us incorporate uncertainty about the membership function into fuzzy set theory. In order to symbolically distinguish between a type-1 fuzzy set and a type-2 fuzzy set, a tilde symbol is put over the symbol for the fuzzy set; so, A denotes a type-1 fuzzy set, whereas à denotes the comparable type-2 fuzzy set. Mendel and Liang [28, 29] characterized T2FSs using the concept of footprint of uncertainty (FOU), and upper and lower MFs. To depict the concept, let us consider type-1 gauss MF shown in ―Fig. 1‖.As can be seen from the figure type-1 gaussian membership function is constrained to be in between 0 and 1 for all x X, and is a two dimensional function. These types of membership don‘t carry any uncertainty. There exists a clear membership value for every input data point.If the Gaussian function in ―Fig.1‖ is blurred ―Fig. 2‖can be obtained. The FOU represents the bounded region obtained by blurring the boundaries of type-1 MF. The upper and lower MFs represent the upper and lower boundaries of the FOU, respectively. In this case, for a specific input value, there is no longer a single certain value of membership; instead the MF takes on values wherever the vertical line intersects the blur. Those values do not have to be all weighted the same; hence, an amplitude distribution can be assigned to those points. Doing this for all input values x, a three dimensional MF is created, which is a type-2 MF. In this, the first two dimensions allow handlingimprecision via modelling the degree of membership of x; while the third dimension allows handling uncertainty via modelling the amplitude distribution of the degree of membership of x. Here also, like in type-1 MFs the degree of membership along the second dimension and the amplitude distribution values along the third dimension is always in the interval [0, 1]. Clearly, if the blur disappears; then a type-2 MF reduces to a type-1 MF.A general architecture of type-2 fuzzy logic system (T2FL) as proposed by Mendel is depicted in ―Fig. 3‖.Fig. 1: A Gaussian Type-1 membership functionFig. 2: A Gaussian Type-2 membership functionFig. 3: A typical type-2 fuzzy logic system [29]Table 5: Example on FP complexity classificationT2FL systems contain five components –rules, fuzzifier, inference engine, type reducer, and defuzzifier. Rules are the heart of a T2FL system, and may be provided by experts or can be extracted from numerical data. These rules can be expressed as a collection of IF-THEN statements. The IF part of a rule is its antecedent, and the THEN part of the rule is its consequent. Fuzzy sets are associated with terms that appear in the antecedents or consequents of rules, and with inputs to and output of the T2FL system. The inference engine combines rules and gives mapping from input type-2 fuzzy sets to output type-2 fuzzy set. The fuzzifier converts inputs into their fuzzy representation. The defuzzifier converts the output of the inference engine into crisp output. The type reducer transforms the type-2 fuzzy output set into type-1 fuzzy set to be processed by the defuzzifier. A T2FL system is very similar to a T1FL system; the major difference being that the output processing block of T1FL system is just a defuzzifier while the output processing block of a T2FL system contains the type reducer as well. III.Problem Description and AnalysisIn cost estimation process, the primary input is the software size and the secondary inputs are the various cost drivers. There is a significant relationship between the software size and cost. There are mainly two types of software size metrics: lines of code (LOC) and Function Point (FP). Size estimation is best done when there is complete information about the system; but this is not available till the system is actually built. The challenge for the estimator is therefore to arrive at a reasonable estimate of the size of the system with partial information.LOC is usually not available until the coding phase, so FP has gained popularity because it can be used at an earlier stage of software development.In our work, we are using type-2 based fuzzy logic approach to calibrate the function point weight values which provides an improvement in the software size estimation process. There are 15 parameters in the FP complexity weight system to calibrate. These parameters are low, average and high values of External Inputs, External Outputs, Internal Logical Files, External Interface Files and External Inquiries respectively. A fuzzy based approach is chosen since it can capture human‘s judgement with ease and instead of giving an exact number to all 15 function points parameters we can define fuzzy linguistic terms and assign a fuzzy set within numeric range. This provides an ability to cope up with the vagueness and imprecision present in the earlier stages of software development.In Function Point Analysis (FPA) method each component is classified to a complexity level determined by the number of its associated files such as DET, RET or FTR as given in Table 4. If we determine the FPA complexity of a particular software application, in some cases it may not correctly reflect the complexity for its components.Table 5 shows a software project with three EIF‘s A, B and C. According to the complexity matrix, A and B are classified as having the same complexity and are assigned the same weight value of 10. However, A has 19 more DET than B and is certainly more complex. But both of them are assigned the same complexity. Also, EIF C is having only one DET less than EIF B and it is classified as average and assigned a weight value of 7. From the above example it is concluded that there is a huge scope of improvement in the FPA complexity classification. Processing the number of FP component associated files such as DET, RET and FTR using fuzzy logic can provide an exact complexity degree.IV.Fuzzy Logic calibration to improve FPAType-2 fuzzy inference system is developed for all the five FPA components (ILF, EIF, EI, EO, EQ) using the Mamdani approach. We define three new linguistic terms: small, medium and large, to express the inputs qualitatively. Also we use linguistic terms: simple, average and complex for the output. To fuzzify the inputs and outputs, we define fuzzy sets to represent the linguistic terms [30]. The fuzzy membership grade is captured through the membership functions of each fuzzy set. The inputs and outputs are represented using gaussian igaussstype2 membership which is represented in ―Fig. 4‖. It has certain mean m, and an uncertain standard deviation that takes on values in [σ1, σ2]. The shaded area represents the FOU. Using interval type-2 Gaussian MF‘s makes it easier to build T2FL systems since the mathematics behind the corresponding inferential procedures and training algorithms are less complicated [29]. ―Fig.5 (a)‖and ―Fig.5 (b)‖ shows how the inputs of EIF are assigned the membership functions and represented using linguistic variables of fuzzy sets. ―Fig. 6‖ depicts the output of EIF using membership functions. After representing the inputs and output of EIF using membership functions nine fuzzy rules are defined using rule editor based on the original complexity matrices and illustrated in Table 6. Each rule has two parts in its antecedent linked with an ‗AND‘ operatorand one part in its consequence. These fuzzy rules define the connection between the input and output fuzzy variables. A fuzzy rule has the form: IF <Antecedent> THEN <Consequent>, where antecedent is a compound fuzzy logic expression of one or more simple fuzzy expressions connected with fuzzy operators; and the consequent is an expression that assigns fuzzy values to output variables. The inference system evaluates all the rules of the rule base and combines the weights of the consequents of all relevantrules in one fuzzy set using the aggregate operation. Finally, the output fuzzy set is defuzzified to a crisp single number.Fig. 4: FOU for Gaussian MFFig. 5 (a): Input fuzzy set DET for EIFFig. 5 (b): Input fuzzy set RET for EIFFig. 6: Output fuzzy set Complexity for EIFTable 6: Truth table of fuzzy logic rule setFig. 7: Type-2 Fuzzy Inference process of Function Points Model Table 7: Calibration using type-2 fuzzy logicAn example of the complete fuzzy inference process is shown in ―Fig. 7‖. Input values are set to DET 51 and RET 5. These are represented using the antecedent part of the fuzzy rules. Finally, the consequent part isdefuzzified and the output is achieved as a single value of 7.63.A fuzzy logic system for each FPA element (ILF, EIF, EI, EO, EQ) is constructed. A fuzzy complexity measurement system that takes into account all five Unadjusted Function Points function components is built after the fuzzy logic system for each function component is established as shown in ―Fig. 8‖. The calibrated values for EIF A, EIF B and EIF C is listed in Table 7 and it is found that these calibrated weight values are more convincing than the original weight values.Fig. 8: Fuzzy complexity measurement system for Type-2 Fuzzyfunction points modelTable 8: Calculation of t2UFFP and UFP for ILFV.Experimental Methodology and ResultsWe have conducted some experiments to develop a type-2 fuzzy system for function points analysis using our framework as depicted in ―Fig. 8‖. Our model has been implemented in Matlab(R2008a). As it is the case with validating any prediction model, real industrial data necessary to use our framework to develop and tune the parameters of prediction models were not available. To get around this data scarcity problem for the sake of showing the validity of our framework for the industry where organizations have their own data available, we generated artificial datasets consisting of 20 projects. A complexity calculation for all the five components for each project is done using the type-2 fuzzy framework. The Tables (8, 9, 10, 11, 12) lists the complexity values for all the five components for the first project using type-2 fuzzy framework (t2UFFP) and conventional method i.e.UFP.Using ―(1)‖ total unadjusted function points from the type-2 technique and the conventional technique is calculated and listed in Table 13. It is found that the type-2 technique is at par than the conventional technique.Table 9: Calculation of t2UFFP and UFP for EIFTable 10: Calculation of t2UFFP and UFP for EITable 11: Calculation of t2UFFP and UFP for EOTable 12: Calculation of t2UFFP and UFP for EQTable 13: Comparison of t2UFFP and UFPTable 14: Comparison of type-2 fuzzy FP and conventional FPIn order to compute the value of the conventional function point and type-2 fuzzy function point, we have treated all the 14 general system characteristics as average. Using ―(2)‖and ―(3)‖VAF and FPA is calculated and listed in Table 14.From the above results it is concluded that the calibrated function points using type-2 fuzzy yields better results than conventional function points.VI.ConclusionsFP as a software size metric is an important topic in the software engineering domain. The use of type2 fuzzy logic to calibrate FP weight values further improves the estimation of FP. This in turn will improve the cost estimation process of software projects. Empirical evaluation has shown that T2FL is promising. But there are potentials for improvements when the framework is deployed in practice. As all the experiments were conducted using artificial datasets, a need to evaluate the prediction performance of the framework on real data still persists. Some future work can be directed towards developing inferential procedures using various other membership functions present in type-2 fuzzy systems. This work can also be extended using Neuro Fuzzy approach. AcknowledgementThe authors would like to thank the anonymous reviewers for their careful reading of this paper and for their helpful comments.References[1] B.W. Boehm. Software Engineering Economics.Prentice Hall, Englewood Cliffs, NJ, 1981.[2] B. Boehm, B. Clark, E. Horowitz, R. Madachy, R.Shelby, C. Westland. Cost models for future software life cycle processes: COCOMO 2.0.Annals of Software Engineering, 1995.[3]L.H. Putnam. A general empirical solution to themacro software sizing and estimation problem.IEEE Transactions on Software Engineering, vol.4, 1978, pp 345-361.[4]Moataz A. Ahmed, Zeeshan Muzaffar. Handlingimprecision and uncertainty in software development effort prediction: A type-2 fuzzylogic based framework. Information and Software Technology Journal. vol. 51, 2009, pp. 640-654. [5]Function Point Counting Practices Manual, fourthedition, International Function Point Users Group, 2004.[6]G. Antoniol, C. Lokan, G. Caldiera, R. Fiutem. Afunction point like measure for object oriented software. Empirical Software Engineering. vol. 4, 1999, pp. 263-287.[7]Fei. Z, X. Liu. f-COCOMO-Fuzzy ConstructiveCost Model in Software Engineering. Proceedings of IEEE International Conference on Fuzzy System. IEEE Press, New York, 1992, pp. 331-337.[8]J. Ryder. Fuzzy Modeling of Software EffortPrediction. Proceedings of IEEE Information Technology Conference. Syracuse, NY, 1998. [9] A.R. Venkatachalam. Software Cost Estimationusing artificial neural networks. Proceedings of the International Joint Conference on Neural Networks, 1993, pp. 987-990.[10]K.K. Shukla. Neuro-genetic Prediction ofSoftware Development Effort. Journal of Information and Software Technology, Elsevier.vol. 42, 2000, pp. 701-713.[11]Alaa.F.Sheta. An Estimation of the COCOMOmodel parameters using the genetic algorithms for the NASA project parameters. Journal of Computer Science, vol. 2, 2006, pp.118 -123. [12]Osias de Souza Lima Junior, Pedro PorfirioMuniaz Parias, Arnaldo Dias Belchior. A fuzzy model for function point analysis to development and enhancement project assessement. CLEI Electronic Journal, vol. 5, 1999, pp. 1-14.[13]Ho Leung, TSOI. To evaluate the function pointanalysis: A case study. International Journal of computer, Internet and management vol. 13, 2005, pp. 31-40.[14]G.R. Finnie, G.E. Wittig, J.M. Desharnais. Acomparison of software effort estimation techniques: using function points with neural networks, case-based reasoning and regression models. Journal of Systems Software, Elsevier.vol. 39, 1977, pp. 281-289.[15]M.A. Al-Hajri, A.A.A Ghani, M.S. Sulaiman,M.H. Selamat. Modification of standard function point complexity weights system. Journal of Systems and Software, Elsevier,vol. 74, 2005, pp.195-206.[16]O.S. Lima, P.F.M. Farias, A.D. Belchior. Fuzzymodeling for function point analysis. Software Quality Journal, vol. 11, 2003, pp. 149-166. [17]C. Yau, H. L. Tsoi. Modelling the probabilisticbehavior of function point analysis. Journal ofInformation and Software Technology, Elsevier.vol. 40, 1998, pp. 59-68.[18]A. Abran, P. Robillard. Function Points Analysis:An empirical study of its measurement processes.IEEE Transactions on Software Engineering, vol.22, 1996, pp.895-910.[19]T. Kralj, I. Rozman, M. Hericko, A. Zivkovic.Improved standard FPA method- resolving problems with upper boundaries in the rating complexity process. Journal of Systems and Software, Elsevier, vol. 77, 2005, pp. 81-90. [20]Wei Xia, Luiz Fernando Capretz, Danny Ho,Faheem Ahmed. A new calibration for function point complexity weights. Journal of Information and Software Technology, Elsevier. vol. 50, 2008 pp.670-683.[21]Mohd. Sadiq, Farhana Mariyam, Aleem Ali,Shadab Khan, Pradeep Tripathi. Prediction of Software Project Effort using Fuzzy Logic.Proceedings of IEEE International Conference on Fuzzy System, 2011, pp. 353-358.[22]A. Albrecht. Measuring application developmentproductivity. Proceedings of the Joint SHARE/GUIDE/IBM Application Development Symposium, 1979, pp. 83-92.[23] L. A. Zadeh. Fuzzy Sets. Information and Control,vol. 8, 1965, pp. 338-353.[24]M. Wasif Nisar, Yong-Ji Wang, Manzoor Elahi.Software Development Effort Estimation using Fuzzy Logic – A Survey. Fifth International Conference on Fuzzy Systems and Knowledge Discovery, 2008, pp 421-427.[25]L. Wang. Adaptive Fuzzy System and Control:Design and Stability Analysis. Prentice Hall, Inc., Englewood Cliffs, NJ 07632, 1994.[26]E.H. Mamdani. Applications of fuzzy algorithmsfor simple dynamic plant. Proceedings of IEEE, vol. 121, 1974, pp. 1585-1588.[27]L. A. Zadeh. The Concept of a Linguistic Variableand Its Application to Approximate Reasoning–1. Information Sciences, vol. 8, 1975, pp. 199-249.[28]J.M. Mendel, Q. Liang. Pictorial comparison ofType-1 and Type-2 fuzzy logic systems.Proceedings of IASTED International Conference on Intelligent Systems and Control, Santa Barbara, CA, October 1999.[29]J.M. Mendel. Uncertain Rule-Based Fuzzy LogicSystems, Prentice Hall, Upper Saddle River, NJ 07458, 2001.[30]E.H. Mamdani. Application of fuzzy logic toapproximate reasoning using linguistic synthesis.IEEE transactions on computers, vol. 26, 1977, pp.1182-1191. Anupama Kaushik is an Assistant Professor at Maharaja Surajmal Institute of Technology, New Delhi, India. Her research area includes Software Engineering, Object Oriented Software Engineering and Soft Computing.Dr. A.K Soni has done his Ph.D. and M.S.(Computer Science) both from Bowling Green State University in Ohio, USA . He is the Professor and Head, Department of Information Technology, Sharda University, Greater Noida, India. His research area includes Software Engineering, Datamining, Database Management Systems and Object Oriented Systems.Dr. Rachna Soni did her M. Phil from IIT Roorkee and Ph.D. from Kururukshetra University, Kurukshetra. She is the Associate Professor and Head, Dept. of Computer Science and Applications, D.A.V. College, Yamunanagar, India. Her area of interest includes Software Risk Management, Project Management, Requirement Engineering, Simulation and Component based Software Engineering.。

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In this paper, we focus on the need for2. This paper proceeds as follow.3. The structure of the paper is as follows.4. In this paper, we shall first briefly introduce fuzzy sets and related concepts5. To begin with we will provide a brief background on theIntroduction1. This will be followed by a description of the fuzzy nature of the problem and a detailed presentation of how the required membership functions are defined.2. Details on xx and xx are discussed in later sections.3. In the next section, after a statement of the basic problem, various situations involving possibility knowledge are investigated: first, an entirely possibility model is proposed; then the cases of a fuzzy service time with stochastic arrivals and non fuzzy service rule is studied; lastly, fuzzy service rule are considered.Review1. This review is followed by an introduction.2. A brief summary of some of the relevant concepts in xxx and xxx is presented in Section 2.3. In the next section, a brief review of the .... is given.4. In the next section, a short review of ... is given with special regard to ...5. Section 2 reviews relevant research related to xx.6. Section 1.1 briefly surveys the motivation for a methodology of action, while 1.2 looks at the difficulties posed by the complexity of systems and outlines the need for development of possibility methods.Body1. Section 1 defines the notion of robustness, and argues for its importance.2. Section 1 devoted to the basic aspects of the FLC decision making logic.3. Section 2 gives the background of the problem which includes xxx4. Section 2 discusses some problems with and approaches to, natural language understanding.5. Section 2 explains how flexibility which often ... can be expressed in terms of fuzzy time window6. Section 3 discusses the aspects of fuzzy set theory that are used in the ...7. Section 3 describes the system itself in a general way, including the ….. and also discusses how to evaluate system performance.8. Section 3 describes a new measure of xx.9. Section 3 demonstrates the use of fuzzy possibility theory in the analysis of xx.10. Section 3 is a fine description of fuzzy formulation of human decision.11. Section 3, is developed to the modeling and processing of fuzzy decision rules12. The main idea of the FLC is described in Section 3 while Section 4 describes the xx strategies.13. Section 3 and 4 show experimental studies for verifying the proposed model.14. Section 4 discusses a previous fuzzy set based approach to cost variance investigation.15. Section 4 gives a specific example of xxx.16. Section 4 is the experimental study to make a fuzzy model of memory process.17. Section 4 contains a discussion of the implication of the results of Section 2 and 3.18. Section 4 applies this fuzzy measure to the analysis of xx and illustrate its use on experimental data.19. Section 5 presents the primary results of the paper: a fuzzy set model ..20. Section 5 contains some conclusions plus some ideas for further work.21. Section 6 illustrates the model with an example.22. Various ways of justification and the reasons for their choice are discussed very briefly in Section 2.23. In Section 2 are presented the block diagram expression of a whole model of human DM system24. In Section 2 we shall list a collection of basic assumptions which a ... scheme must satisfy.25. In Section 2 of this paper, we present representation and uniqueness theorems for the fundamental measurement of fuzziness when the domain of discourse is order dense.26. In Section 3, we describe the preliminary results of an empirical study currently in progress to verify the measurement model and to construct membership functions.27. In Section 5 is analyzed the inference process through the two kinds of inference experiments... This Section1. In this section, the characteristics and environment under which MRP is designed are described.2. We will provide in this section basic terminologies and notations which are necessary for the understanding of subsequent results.Next Section2. The next section describes the mathematics that goes into the computer implementation of such fuzzy logic statements.3. However, it is cumbersome for this purpose and in practical applications the formulae were rearranged and simplified as discussed in the next section.4. The three components will be described in the next two section, and an example of xx analysis ofa computer information system will then illustrate their use.5. We can interpret the results of Experiments I and II as in the following sections.6. The next section summarizes the method in a from that is useful for arguments based on xxSummary1. This paper concludes with a discussion of future research consideration in section 5.2. Section 5 summarizes the results of this investigation.3. Section 5 gives the conclusions and future directions of research.4. Section 7 provides a summary and a discussion of some extensions of the paper.5. Finally, conclusions and future work are summarized6. The basic questions posed above are then discussed and conclusions are drawn.7. Section 7 is the conclusion of the paper.Chapter 0. Abstract1. A basic problem in the design of xx is presented by the choice of a xx rate for the measurement of experimental variables.2. This paper examines a new measure of xx in xx based on fuzzy mathematics which overcomes the difficulties found in other xx measures.3. This paper describes a system for the analysis of the xx.4. The method involves the construction of xx from fuzzy relations.5. The procedure is useful in analyzing how groups reach a decision.6. The technique used is to employ a newly developed and versatile xx algorithm.7. The usefulness of xx is also considered.8. A brief methodology used in xx is discussed.9. The analysis is useful in xx and xx problem.10. A model is developed for a xx analysis using fuzzy matrices.11. Algorithms to combine these estimates and produce a xx are presented and justified.12. The use of the method is discussed and an example is given.13. Results of an experimental applications of this xx analysis procedure are given to illustrate the proposed technique.14. This paper analyses problems in15. This paper outlines the functions carried out by ...16. This paper includes an illustration of the ...17. This paper provides an overview and information useful for approaching18. Emphasis is placed on the construction of a criterion function by which the xx in achieving a hierarchical system of objectives are evaluated.19. The main emphasis is placed on the problem of xx20. Our proposed model is verified through experimental study.21. The experimental results reveal interesting examples of fuzzy phases of: xx, xx22. The compatibility of a project in terms of cost, and xx are likewise represented by linguistic variables.23. A didactic example is included to illustrate the computational procedureChapter 1. IntroductionTime1. Over the course of the past 30 years, .. has emerged form intuitive2. T echnological revolutions have recently hit the industrial world3. The advent of ... systems for has had a significant impact on the4. The development of ... is explored5. During the past decade, the theory of fuzzy sets has developed in a variety of directions6.The concept of xx was investigated quite intensively in recent years7. There has been a turning point in ... methodology in accordance with the advent of ...8. A major concern in ... today is to continue to improve...9. A xx is a latecomer in the part representation arena.10. At the time of this writing, there is still no standard way of xx11. Although a lot of effort is being spent on improving these weaknesses, the efficient and effective method has yet to be developed.12. The pioneer work can be traced to xx [1965].13. To date, none of the methods developed is perfect and all are far from ready to be used in commercial systems.Objective / Goal / Purpose1. The purpose of the inference engine can be outlined as follows:2. The ultimate goal of the xx system is to allow the non experts to utilize the existing knowledge in the area of manual handling of loads, and to provide intelligent, computer aided instruction for xxx.3. The paper concerns the development of a xx4. The scope of this research lies in5. The main theme of the paper is the application of rule based decision making.6. These objectives are to be met with such thoroughness and confidence as to permit ...7. The objectives of the ... operations study are as follows:8. The primary purpose/consideration/objective of9. The ultimate goal of this concept is to provide10. The main objective of such a ... system is to11. The aim of this paper is to provide methods to construct such probability distribution.12. In order to achieve these objectives, an xx must meet the following requirements:13. In order to take advantage of their similarity14. more research is still required before final goal of ... can be completed15. In this trial, the objective is to generate...16. for the sake of concentrating on ... research issues17. A major goal of this report is to extend the utilization of a recently developed procedure for the xx.18. For an illustrative purpose, four well known OR problems are studied in presence of fuzzy data: xx.19. A major thrust of the paper is to discuss approaches and strategies for structuring ..methods20. This illustration points out the need to specify21. The ultimate goal is both descriptive and prescriptive.22. Chapter 2. Literature Review23. A wealth of information is to be found in the statistics literature, for example, regarding xx24. A considerable amount of research has been done .. during the last decade25. A great number of studies report on the treatment of uncertainties associated with xx.26. There is considerable amount of literature on planning27. However, these studies do not provide much attention to uncertainty in xx.28. Since then, the subject has been extensively explored and it is still under investigation as well in methodological aspects as in concrete applications.29. Many research studies have been carried out on this topic.30. Problem of xx draws recently more and more attention of system analysis.31. Attempts to resolve this dilemma have resulted in the development of32. Many complex processes unfortunately, do not yield to this design procedure and have, therefore, not yet been automated.33. Most of the methods developed so far are deterministic and /or probabilistic in nature.34. The central issue in all these studies is to35. The problem of xx has been studied by other investigators, however, these studies have been based upon classical statistical approaches.36. Applied ... techniques to37. Characterized the ... system as38. Developed an algorithm to39. Developed a system called ... which40. Uses an iterative algorithm to deduce41. Emphasized the need to42. Identifies six key issues surrounding high technology43. A comprehensive study of the... has been undertaken44. Much work has been reported recently in these filed45. Proposed/Presented/State that/Described/Illustrated/Indicated/Has shown / showed/Address/Highlights46. Point out that the problem of47. A study on ...was done / developed by []48. Previous work, such as [] and [], deal only with49. The approach taken by [] is50. The system developed by [] consists51. A paper relevant to this research was published by []52. []'s model requires consideration of...53. []' model draws attention to evolution in human development54. []'s model focuses on...55. Little research has been conducted in applying ... to56. The published information that is relevant to this research...57. This study further shows that58. Their work is based on the principle of59. More history of ... can be found in xx et al. [1979].60. Studies have been completed to established61. The ...studies indicated that62. Though application of xx in the filed of xx has proliferated in recent years, effort in analyzing xx, especially xx, is lacking.Problem / Issue / Question63. Unfortunately, real-world engineering problems such as manufacturing planning do not fit well with this narrowly defined model. They tend to span broad activities and require consideration of multiple aspects.64. Remedy / solve / alleviate these problems67. ... is a difficult problem, yet to be adequately resolved68. T wo major problems have yet to be addressed69. An unanswered question70. This problem in essence involves using x to obtain a solution.71. An additional research issue to be tackled is ....72. Some important issues in developing a ... system are discussed73. The three prime issues can be summarized:74. The situation leads to the problem of how to determine the ...75. There have been many attempts to76. It is expected to be serious barrier to77. It offers a simple solution in a limited domain for a complex。

Fuzzy Set Theory by Shin-Yun WangBefore illustrating the fuzzy set theory which makes decision under uncertainty, it is important to realize what uncertainty actually is.Uncertainty is a term used in subtly different ways in a number of fields, including philosophy, statistics, economics, finance, insurance, psychology, engineering and science. It applies to predictions of future events, to physical measurements already made, or to the unknown. Uncertainty must be taken in a sense radically distinct from the familiar notion of risk, from which it has never been properly separated.... The essential fact is that 'risk' means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating.... It will appear that a measurable uncertainty, or 'risk' proper, as we shall use the term, is so far different from an immeasurable one that it is not in effect an uncertainty at all.What is relationship between uncertainty, probability, vagueness and risk? Risk is defined as uncertainty based on a well grounded (quantitative) probability. Formally, Risk = (the probability that some event will occur) X (the consequences if it does occur). Genuine uncertainty, on the other hand, cannot be assigned such a (well grounded) probability. Furthermore, genuine uncertainty can often not be reduced significantly by attempting to gain more information about the phenomena in question and their causes. Moreover the relationship between uncertainty, accuracy, precision, standard deviation, standard error, and confidence interval is that the uncertainty of a measurement is stated by giving a range of values which are likely to enclose the true value. This may be denoted by error bars on a graph, or as value ± uncertainty, or as decimal fraction (uncertainty).Often, the uncertainty of a measurement is found by repeating the measurement enough times to get a good estimate of the standard deviation of the values. Then, any single value has an uncertainty equal to the standard deviation. However, if the values are averaged and the mean is reported, then the averaged measurement has uncertainty equal to the standard error which is the standard deviation divided by the square root of the number of measurements. When the uncertainty represents the standard error of the measurement, then about 68.2% of the time, the true value of the measured quantity falls within the stated uncertainty range.Therefore no matter how accurate our measurements are, some uncertainty always remains. The possibility is the degree that thing happens, but the probability is theprobability that things be happen or not. So the methods that we deal with uncertainty are to avoid the uncertainty, statistical mechanics and fuzzy set (Zadeh in 1965).(Figure from Klir&Yuan)Fuzzy sets have been introduced by Lotfi A. Zadeh (1965). What Zadeh proposed is very much a paradigm shift that first gained acceptance in the Far East and its successful application has ensured its adoption around the world. Fuzzy sets are an extension of classical set theory and are used in fuzzy logic. In classical set theory the membership of elements in relation to a set is assessed in binary terms according to a crisp condition — an element either belongs or does not belong to the set. By contrast, fuzzy set theory permits the gradual assessment of the membership of elements in relation to a set; this is described with the aid of a membership function valued in the real unit interval [0, 1]. Fuzzy sets are an extension of classical set theory since, for a certain universe, a membership function may act as an indicator function, mapping all elements to either 1 or 0, as in the classical notion.Specifically, A fuzzy set is any set that allows its members to have different grades of membership (membership function) in the interval [0,1]. A fuzzy set on a classical set Χ is defined as follows:The membership function μA (x ) quantifies the grade of membership of the elements x to the fundamental set Χ. An element mapping to the value 0 means that the member is not included in the given set, 1 describes a fully included member. Values strictly between 0 and 1 characterize the fuzzy members.Membership function terminology Universe of Discourse: the universe of discourse is the range of all possible values for an input to a fuzzy system. Support: the support of a fuzzy set F is the crisp set of all points in the universe of discourse U such that the membership function of F is non-zero.Core: the core of a fuzzy set F is the crisp set of all points in the universe of discourseU such that the membership function of F is 1.Supp {|()0, X}A A x x x μ=>∀∈core {|()1, X}A A x x x μ==∀∈Boundaries: the boundaries of a fuzzy set F is the crisp set of all points in the universe of discourse U such that the membership function of F is between 0 and 1. Crossover point: the crossover point of a fuzzy set is the element in U at which its membership function is 0.5. Height: the biggest value of membership functions of fuzzy set. Normalized fuzzy set: the fuzzy set of Cardinality of the set:Relative cardinality:Convex fuzzy set: , a fuzzy set A is Convex, if forType of membership functions1. Numerical definition (discrete membership functions)()/i A i i x X A x x μ∈=∑2. Function definition (continuous membership functions)Including of S function, Z Function, Pi function, Triangular shape, Trapezoid shape, Bell shape.()/A XA x x μ=⎰(1) S function: monotonical increasing membership function220 2() (;,,)12() 1 x x for x for x S x for x for xαγααγαααβαβγβγγ----≤⎧⎪≤≤⎪=⎨-≤≤⎪⎪≤⎩()0.5x μ=Boundaries {|0()1, X}A A x x x μ=<<∀∈Height()1A =A A X Supp()X : ()()x x A finiteA x x μμ∈∈==∑∑X AA =X R ∈[0, 1]λ∀∈1212((1))min((), ())A A A x x x x μλλμμ+-≥(2) Z function: monotonical decreasing membership function(3) ∏ function: combine S function and Z function, monotonical increasing and decreasing membership functionPiecewise continuous membership function(4)Trapezoidal membership function(5) Triangular membership function(6) Bell-shaped membership function11a 1b a 011a 1b b a 221 12() (;,,)2() 0 x x for x for x Z x for x for xαγααγαααβαβγβγγ----≤⎧⎪-≤≤⎪=⎨≤≤⎪⎪≤⎩22(; , , ) (;,)1(; , , ) S x for x x S x for x ββγβγγγβγγγγβγ⎧--≤⎪∏=⎨-++≥⎪⎩111111110 ()1 0 x a a a A b x b b for x a for a x a x for a x b for b x b for b xμ----≤⎧⎪≤≤⎪⎪=≤≤⎨⎪≤≤⎪⎪≤⎩111111110 () 0 x a a a A b x b a for x a for a x a x for a x b for b xμ----≤⎧⎪≤≤⎪=⎨≤≤⎪⎪≤⎩Before illustrating the mechanisms which make fuzzy logic machines work, it is important to realize what fuzzy logic actually is. Fuzzy logic is a superset of conventional (Boolean) logic that has been extended to handle the concept of partial truth- truth values between "completely true" and "completely false". As its name suggests, it is the logic underlying modes of reasoning which are approximate rather than exact. The importance of fuzzy logic derives from the fact that most modes of human reasoning and especially common sense reasoning are approximate in nature. The essential characteristics of fuzzy logic are as follows.• In fuzzy logic, exact reasoning is viewed as a limiting case of approximate reasoning.•In fuzzy logic everything is a matter of degree.• Any logical system can be fuzzified.• In fuzzy logic, knowledge is interpreted as a collection of elastic or, equivalently, fuzzy constraint on a collection of variables.• Inference is viewed as a process of propagation of elastic constraints. After know about the characteristic of fuzzy set, we will introduce the operations of fuzzy set. A fuzzy number is a convex, normalized fuzzy set whose membership function is at least segmental continuous and has the functional value μA (x ) = 1 at precisely one element. This can be likened to the funfair game "guess your weight," where someone guesses the contestants weight, with closer guesses being more correct, and where the guesser "wins" if they guess near enough to the contestant's weight, with the actual weight being completely correct (mapping to 1 by the membership function). A fuzzy interval is an uncertain set with a mean interval whose elemen ts possess the membership function value μA (x ) = 1. As in fuzzy numbers, the membership function must be convex, normalized, and at least segmental continuous.Set- theoretic operationsSubset: A B A B μμ⊆⇔≤ Complement: ()1()A A A X A x x μμ=-⇔=-Union: ()max((),())()()c A B A B C A B x x x x x μμμμμ=⋃⇔==∨Intersection: ()min((),())()()c A B A B C A B x x x x x μμμμμ=⋂⇔==∧Although one can create fuzzy sets and perform various operations on them, in general they are mainly used when creating fuzzy values and to define the linguistic terms of fuzzy variables. This is described in the section on fuzzy variables. At some point it may be an interesting exercise to add fuzzy numbers to the toolkit. These would be specializations of fuzzy sets with a set of operations such as addition, subtraction, multiplication and division defined on them.According to the characteristics of triangular fuzzy numbers and the extension principle put forward by Zadeh (1965), the operational laws of triangular fuzzy numbers , 111(,,)A l m r =and 222(,,)B l m r =are as follows:(1) Addition of two fuzzy numbers111222121212(,,)(,,)(,,)l m r l m r l l m m r r ⊕=+++(2) Subtraction of two fuzzy numbers111222121212(,,)(,,)(,,)l m r l m r l r m m r l Θ=---(3) Multiplication of two fuzzy numbers111222121212(,,)(,,)(,,)l m r l m r l l m m rr ⊗≅(4) Division of two fuzzy numbers111222121212(,,)(,,)(/,/,/)l m r l m r l r m m r l ∅≅When we through the operations of fuzzy set to get the fuzzy interval, next we will convert the fuzzy value into the crisp value. Below are some methods that convert a fuzzy set back into a single crisp (non-fuzzy) value. This is something that is normally done after a fuzzy decision has been made and the fuzzy result must be used in the real world. For example, if the final fuzzy decision were to adjust the temperaturesetting on the thermostat a ‘little higher’, then it would be necessary to convert this ‘little higher’ fuzzy value to the ‘best’ crisp value to actually move the thermost at setting by some real amount.Maximum Defuzzify: finds the mean of the maximum values of a fuzzy set as the defuzzification value. Note: this doesn't always work well because there can be x ranges where the y value is constant at the max value and other places where the maximum value is only reached for a single x value. When this happens the single value gets too much of a say in the defuzzified value.Moment Defuzzify: moment defuzzifies a fuzzy set returning a floating point (double value) that represents the fuzzy set. It calculates the first moment of area of a fuzzy set about the y axis. The set is subdivided into different shapes by partitioning vertically at each point in the set, resulting in rectangles, triangles, and trapezoids. The centre of gravity (moment) and area of each subdivision is calculated using the appropriate formulas for each shape. The first moment of area of the whole set is then:where x i' is the local centre of gravity, A i is the local area of the shape underneath line segment (p i-1, p i), and n is the total number of points. As an example,For each shaded subsection in the diagram above, the area and centre of gravity is calculated according to the shape identified (i.e., triangle, rectangle or trapezoid). The centre of gravity of the whole set is then determined:x' = (2.333*1.0 + 3.917*1.6 + 5.5*0.6 + 6.333*0.3)/(1.0+1.6+0.6+0.3) = 3.943…Center of Area (COA): defuzzification finds the x value such that half of the area under the fuzzy set is on each side of the x value. In the case above (in the moment defuzzify section) the total area under the fuzzy set is 3.5 (1.0+1.6+0.6+0.3). So we would want to find the x value where the area to the left and the right both had values of 1.75. This occurs where x = . Note that in general the results of moment defuzzify and center of area defuzzify are not the same. Also note that in some cases the center of area can be satisfied by more than one value. For example, for the fuzzy set defined by the points:(5,0) (6,1) (7,0) (15,0) (16,1) (17,0)the COA could be any value from 7.0 to 15.0 since the 2 identical triangles centered at x=6 and x=16 lie on either side of 7.0 and 15.0. We will return a value of 11.0 in this case (in general we try to find the middle of the possible x values).Weighted Average Defuzzify: finds the weighted average of the x values of the points that define a fuzzy set using the membership values of the points as the weights. This value is returned as the defuzzification value. For example, if we have the following fuzzy set definition:Then the weighted average value of the fuzzy set points will be:This is only moderately useful since the value at 1.0 has too much influence on the defuzzified result. The moment defuzzification is probably most useful in this case. However, a place where this defuzzification method is very useful is when the fuzzy set is in fact a series of singleton values. It might be that a set of rules is of the Takagi-Sugeno-Kang type (1st order) with formats like:If x is A and y is B then c = kwhere x and y are fuzzy variables and k is a constant that is represented by a singleton fuzzy set. For example we might have rules that look like:where the setting of the hot valve has several possibilities, say full closed, low, medium low, medium high, high and full open, and these are singleton values rather than normal fuzzy sets. In this case medium low might be 2 on a scale from 0 to 5.An aggregated conclusion for setting the hot valve position (after all of the rules have contributed to the decision) might look like:And the weighted average defuzzification value for this output would be:Note that neither a maximum defuzzification nor a moment defuzzification would produce a useful result in this situation. The maximum version would use only 1 of the points (the maximum one) giving a result of 2.0 (the x value of that point), while the moment version would not find any area to work with and would generate an exception. This description of the weighted average defuzzify method will be clearer after you have completed the sections on fuzzy values and fuzzy rules.After the process of defuzzified, next step is to make a fuzzy decision. Fuzzy decision which is a model for decision making in a fuzzy environment, the object function and constraints are characterized as their membership functions, the intersection of fuzzy constraints and fuzzy objection function. Fuzzy decision-making method consists of three main steps:1.Representation of the decision problem: the method consists of three activities. (1)Identifying the decision goal and a set of the decision alternatives. (2) Identifyinga set of the decision criteria. (3) Building a hierarchical structure of the decisionproblem under consideration2.Fuzzy set evaluation of decision alternatives: the steps consist of three activities.(1) Choosing sets of the preference ratings for the importance weights of thedecision preference ratings include linguistic variable and triangular fuzzy number.(2) Evaluating the importance weights of the criteria and the degrees ofappropriateness of the decision alternatives. (3) Aggregating the weights of the decision criteria.3.Selection of the optimal alternative: this step includes two activities. (1)Prioritization of the decision alternatives using the aggregated assessments. (2) Choice of the decision alternative with highest priority as the optimal.Applications of fuzzy set theory:An innovative method based on fuzzy set theory has been developed that can accurately predict market demand on goods. Based on the fuzzy demand function and fuzzy utility function theories, two real-world examples have been given to demonstrate the efficacy of the theory.Example:I.Brief Background on Consumption Theory1. Consumer Behaviors and PreferenceOne consumer would in general have different consumption behaviors or preferences from another. He may spend money on computers and technical books, while the other may spend on clothing and food. Availability of this information on consumer preference will be of great value to a marketing company, a bank, or a credit card company that can use this information to target different groups of consumer for improved response rate or profit. By the same token, information on consumption preference of the residents in one specific region can help businesses in planning their operations in this region for improved profit. Therefore, it is very important to have a tool that can help analyze consumers’ behaviors and forecast the changes in purchase patterns and changes in purchase trend.2. Fuzzy Consumption Utility Functions-based Utility TheoryIn studying advanced methodology for consumption behaviors, AI researchers at Zaptron Systems have developed the so called fuzzy utility functions that can model and describe the consumption behaviors of a target consumer group.3. Consumption Utility - it is a criterion (or index) used to evaluate the effectiveness of customers consumption. A low value of consumption utility, say 0.15 indicates that a customer is not satisfied with the consumption of a certain commodity; while high value, say 0.96, indicates that the customer is very satisfied. There are formal theories on utility, including ordinal utility, cardinal utility and marginal utility.4. Consumption utility function - The behavioral characteristics of human beings can be represented by the concept of consumption utility, and consumption utility function is the mathematical description of this concept. In addition, human consumption behaviors are determined by the following two types of factors:(1) Objective factors - the physical, chemical, biological and artistic properties ofgoods;(2) Subjective factors - consumer's interest, preference and psychological state.5. Because of the objective and subjective factors, the fuzzy utility function for consumption can use the fuzzy set theoretical approach -- in fact, consumption utility is a fuzzy concept. To model the above subjective factors, fuzzy set theory is used to describe different levels of consumers’ satisfaction with respect to various consumption plans (spending patterns), such as "not satisfied," "somehow satisfied," "very satisfied," and etc. Mathematically, the fuzzy utility function is a more accurate measure on the consumption utility. It can describe the relationships among spending, price, consumption composition (decomposition), preference and subjective measure on commodity or service values.II.Brief Background on Demand Theory1. Consumption Demand - it is the amount of consumption on goods (purchase amount). In general, it is related to the objective factors of commodities (such as physical, chemical and artistic characters) and the subjective value of the consumer (preference, personal habits, health conditions, etc.). Demand is affected by the total spending capability and population of a customer group, as well as the consumer prices.2. Consumption Demand Function - the behavioral characteristics of financial market can be represented by the concept of consumption demand and the consumption demand function is the mathematical description of this concept. In addition, consumption demand can be determined by the following types of factors:(1) Objective factors - the physical, chemical, biological and artistic properties ofgoods;(2) Subjective factors - consumer's interest, preference and psychological state;(3) Group factors - population and wealth of the consumers (consumer group);(4) Comparative factors - the ratio of prices of different goods, ratio of differentpreference, and ratio of subjective values on(i) Different goods (comparisons of different consumption can directly affect theconsumption demand);(ii) Fluctuation factors - wealth, population and price fluctuations.3. Because of the objective, subjective, group and comparative factors, the fuzzy consumption demand functions can use the fuzzy set theoretical approach-- in studying advanced methodology for the analysis of consumption demand, AI researchers at Zaptron Systems have developed technology and software tool based on the so called fuzzy demand functions. They can model and describe the market demand, or consumption demand, on various commodities or services, based on consumption data available. The fuzzy demand functions discussed here are developed based on the fuzzy consumption utility function theory developed by Zaptron scientists.4. In fact, consumption demand is a fuzzy logic concept. Mathematically, the fuzzy demand function is a more accurate measure on the consumption demand, compared against a traditional (non-fuzzy) demand function. It can describe relationships among wealth, price, consumption composition (decomposition), preference and subjective measure on commodity or service values. Computation of fuzzy demand functions and parameters - based on the maximum utility principle, they can be computed by solving a set of complex mathematical equations. From above examples, an innovative method based on fuzzy set theory has been developed that can accurately predict market demand on goods. Based on the fuzzy demand function and fuzzy utility function theories have been given to demonstrate the efficacy of the theory.III.Brief Background on Option Theory1. Option pricing model: the optimal option price has been used to compute by the binomial model (1979) or the Black-Scholes model (1973). However, volatility and riskless interest rate are assumed as constant in those models. Hence, many subsequent studies emphasized the estimated riskless interest rate and volatility. Cox (1975) introduced the concept of Constant-Elasticity-of-Variance for volatility. Hull and White (1987) released the assumption that the distribution of price of underlying asset and volatility are constant. Wiggins (1987), Scott (1987), Lee, Lee and Wei (1991) released the assumption that the volatility is constant and assumedthat the volatility followed Stochastic-Volatility.Amin (1993) and Scott (1987) considered that the Jump-Diffusion process of stock price and the volatility were random process. Researchers have so far made substantial effort and achieve significant results concerning the pricing of options (e.g., Brennan and Schwartz, 1977; Geske and Johnson, 1984; Barone-Adesi and Whaley, 1987). Empirical studies have shown that given their basic assumptions, existing pricing model seem to have difficulty in properly handling the uncertainties inherent in any investment process.2. There are five primary factors affecting option prices. These are striking price, current stock price, time, riskless interest rate, and volatility. Since the striking price and time until option expiration are both determined, current stock prices reflect on ever period, but riskless interest rate determined the interest rate of currency market, and volatility can’t be observed directly but can be estimated by historical data and situation analysis. Therefore, riskless interest rate and volatility are estimated. The concept of fuzziness can be used to estimate the two factors riskless interest rate and volatility.3. Fuzzy option pricing model: because most of studies have focused on how to release the assumptions in the CRR model and the B-S model, including: (1) the short-term riskless interest rate is constant, (2) the volatility of a stock is constant. After loosening these assumptions, the fuzzy set theory applies to the option pricing model, in order to replace the complex models of previous studies. (Lee, Tzeng and Wang, 2005).4. As derivative-based financial products become a major part of current global financial market, it is imperative to bring the basic concepts of options, especially the pricing method to a level of standardization in order to eliminate possible human negligence in the content or structure of the option market. The fuzzy set theory applies to the option pricing model (OPM) can providing reasonable ranges of option prices, which many investors can use it for arbitrage or hedge.ReferencesAmin, K. I. (1993). Jump diffusion option valuation in discrete time. Journal of Finance, 48(5), 1833–1863.Barone-Adesi, G. and R. E. Whaley (1987). Efficient analytic approximation of American option values. Journal of Finance, 42(2), 301–320.Black, F., and M. Scholes (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637–654.Brennan, M. J. and E. S. Schwartz (1977). The valuation of American put options. Journal of Finance, 32(2), 449–462.Cox, J. C. and S. A. Ross (1975). Notes on option pricing I: Constant elasticity of variance diffusion. Working paper. Stanford University.Cox, J. C., S. A. Ross, and M. Rubinstein (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229–263.Lee, C.F., G.H. Tzeng, and S.Y. Wang (2005). A new application of fuzzy set theory to the Black-Scholes option pricing model. Expert Systems with Applications, 29(2), 330-342.Lee, C.F., G.H. Tzeng, and S.Y. Wang (2005). A Fuzzy set approach to generalize CRR model: An empirical analysis of S&P 500 index option. Review of Quantitative Finance and Accounting, 25(3), 255-275.Lee, J. C., C. F. Lee, and K. C. J. Wei (1991). Binomial option pricing with stochastic parameters: A beta distribution approach. Review of Quantitative Finance and Accounting, 1(3), 435–448.Goguen, J. A. (1967). L-fuzzy sets. Journal of Mathematical Analysis and Applications, 18, 145–174.Geske, R. and H. E. Johnson (1984). The american put valued analytically. Journal of Finance, 1511–1524.Gottwald, S. (2001). A Treatise on Many-Valued Logics. Baldock, Hertfordshire, England: Research Studies Press Ltd.Hull, J. and A. White (1987). The pricing of options on assets with stochastic volatilities. Journal of Finance, 42(2), 281–300.Klir, G.J. and B. Yuan. (1995). Fuzzy Sets and Fuzzy Logic. Theory. and Applications, Ed. Prentice-Hall.Scott, L. (1987). Option pricing when variance changes randomly: Theory, estimation and an application. Journal of Financial and Quantitative Analysis, 22(4), 419–438.Wiggins, J. B. (1987). Option values under stochastic volatility: Theory and empirical evidence. Journal of Financial Economics, 19(2), 351–372.Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning. Information Sciences, 8,199–249, 301–357; 9, 43–80.Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. 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A fuzzy constraint satisfaction approach for electronic shopping assistanceJuite Wang a,*,C.-H.Dai b,1aDepartment of Industrial Engineering,Feng Chia University,100Wenhwa Road,P.O.Box 25-097,Taichung 407,Taiwan,ROC bCustomer Service Department,Total Logistics Support Section,Aerospace Industrial Development Corporation,No.111-19,Lane 68,Fu-Hsing N.Road,Taichung 407,Taiwan,ROCAbstractThe Internet and World Wide Web offer an additional channel for consumers to find,select,and buy products.However,unlike shopping in the traditional store,consumers have no direct contact with human clerks to get the required information in the electronic store.The objective of this paper is to propose a fuzzy constraint satisfaction approach to help buyers find fully satisfactory or replacement products in electronic shopping.For the buyer who can give precise product requirements,the proposed approach can generate product-ranking lists based on the satisfaction degrees of each product to the given requirements.For the buyer who may not input accurate requirements,a similarity analysis approach is proposed to assess buyer requirements automatically during his browsing process.The proposed approach could help buyers find the preferred products on the top of the ranking list without further searching the remaining pages.The experimental results show the applicability of the proposed approach for electronic shopping assistance.q 2004Elsevier Ltd.All rights reserved.Keywords:Electronic commerce;Fuzzy sets;Constraint satisfaction;Similarity measures;Possibility theory1.IntroductionThe Internet and World Wide Web are becoming increasingly important channels to offer consumers a simple way to find,select,and buy products (NUA Internet Surveys,2002).However,the shopping behavior of consumers in the electronic shop is quite different from the traditional shopping store.Since consumers have no direct contact with the human clerk to get the required information,they have to find the required product information by themselves to make purchasing decisions.Therefore,it is important to provide useful information (e.g.electronic catalogs)or mechanism (e.g.search engines)to assist consumers in electronic shopping (Changchien &Lu,2001;Lee,Liu,&Lu,2002;Lee &Widmeyer,1998;Ryu,1999;Stanoevska-Slabeva &Schmid,2000;Yuan &Liu,2000).Electronic catalog is the most commonly used for the electronic store (Stanoevska-Slabeva &Schmid,2000).Product information in the electronic catalog is not only textual description of a product,but also pictures of a product or even its animation.However,if product information is poor organized,it is hard to find satisfactory products for buyers (NUA Internet Surveys,1999b ).Some of the electronic stores provide search mechanisms by entering keywords or product requirements to help buyers find satisfactory products.However,if there is no exactly matched product with the keywords or product requirements provided by buyers,no suitable product can be found.NUA Internet Surveys (1999a)also reported that the advertised online products that were not actually in stock caused that one in 10orders could not be fulfilled.In fact,the satisfaction of a buyer requirement may not be strictly either ‘true’or ‘false’,but should be a degree within a range.For example,a buyer may specify that the weight of the notebook computer that he is interested in should be less than or equal to 3.0kg.Assume that there are two products A and B with weights 2.9and 2.8,respectively.Although both products satisfy the requirement,product B should be preferred to product A ,if the values of other attributes for two products are all the same.In addition,if a buyer has poor understanding of product specifications or even his preferences,he may not find desirable products.0957-4174/$-see front matter q 2004Elsevier Ltd.All rights reserved.doi:10.1016/j.eswa.2004.06.004Expert Systems with Applications 27(2004)593–607/locate/eswa*Corresponding author.Tel.:C 886-4-2451-7250x3636;fax:C 886-4-2451-0240.E-mail addresses:rdwang@.tw (J.Wang),chiahaodai@ (C.-H.Dai).1Tel.:C 886-4-2707-0001x502557.Therefore,it is required to have mechanisms to assist the buyer infinding the products that can fulfill his needs completely or partially.Several researches have been devoted to develop methods for the electronic shopping assistance.Doorenbos, Etzioni,and Weld(1997)developed a comparison-shopping agent to gather product/merchant information auto-nomously from the web to buyers and buyers can make their purchasing decision quickly.Lee and Widmeyer (1998)developed a search mechanism based on a taxonomy hierarchy to select a product closest to the requested product,as the requested product is in short supply.Ryu (1999)extended their work to allow buyers to select more desirable replacement product using the hierarchical con-straint satisfaction approach,but did not consider the partial satisfaction of a product to the buyer requirement.In recent year,some researchers applied data mining or soft computing techniques to analyze the sales databases or available personal purchasing profiles to obtain more information for purchasing recommendation.Yuan and Liu(2000)integrated the reinforcement learning and artificial neural networks to learn buyer preferences in every interaction session and generated customized product-ranking lists based on the preferences learned.However, using the learning approach needs numerous interactions to learn accurate buyer preferences.The preference profile learned may not be for later use or for different product categories,because the buyer preference may be different for different time horizon or product categories.Changchien and Lu(2001)applied artificial neural networks and rough set theory to extract buying habits from sales database to support on-line purchasing recommendation.Lee et al. (2002)developed a genetic algorithm approach to analyze personal purchasing profile and made recommendations to consumers for frequently purchasing products(e.g.books, CD).For the products that are seldom purchased by consumers(e.g.notebook computers,home theater sys-tems),they also proposed a multi-criteria decision-making approach(Chen,Hwang,&Hwang,1992)for purchasing recommendation to a buyer without analyzing the buyer’s purchasing profiles for this type of products(Lee et al.).In summary,for the products that are seldom purchased by consumers,it is not meaningful to analyze consumer’s purchasing profiles,because the past purchasing records may not be enough or consumer’s preferences may change. In addition,using on-line learning approaches to extract the requirements of a buyer from the buyer browsing process may be not practical for this type of products,because it may requires numerous interactions to learn accurate buyer requirements.The objective of this paper is to develop a fuzzy constraint satisfaction approach to help buyers tofind fully satisfactory or replacement products that are infrequently purchased.Each buyer requirement is con-sidered as a constraint to guide the product selection.Since the satisfaction of a buyer requirement may not be true or false,fuzzy set theory(Klir&Yuan,1995)is used to measure the satisfaction degree of a product to each buyer requirement.It also allows novice buyers who may not be familiar with the purchasing products to specify their needs in linguistic terms.According to buyer requirements given directly by the buyer,the proposed approach generates a product-ranking list based on the satisfaction level of each product to the buyer requirements.In addition,since buyers may not always fully understand their needs of the purchasing products or they may not input accurate buyer requirements,a similarity analysis approach is proposed to assess the buyer requirements automatically during every interaction.According to the buyer requirements estimated, a new product-ranking list can is generated to help the buyer find desirable products on the top of the ranking list without further searching the remaining pages of the list.The paper is organized as follows.Section2describes the electronic shopping assistance problem.The proposed methodology and the system framework are presented in Sections3and4,respectively.Section5shows experimental results of the proposed approach.Finally,Section6 concludes the paper.The basic concept of fuzzy set theory is introduced in Appendix A.2.Modeling the electronic shopping assistance problemLet P Z{P1,P2,.,P m}be the set of products in the electronic store and each product P i2P is characterized by the set X Z{X1,X2,.,X n}of measurable attributes,where each attribute has a domain specifying the set of legal values.Let R Z{R1,R2,.,R n}be the set of buyer require-ments and W Z{w1,w2,.,w n}be the set of relative importance for attributes of X.The buyer requirements and the corresponding relative importance may be specified explicitly or implicitly by the buyer.In this paper,each buyer requirement is considered as a constraint and the satisfaction level of a product P i2P to a buyer requirement R i2R is measured as a degree within[0,1].A fuzzy constraint satisfaction approach is proposed to generate a product-ranking list that orders the set P of products based on their satisfaction levels and relative importance of each attribute to assist buyers infinding desirable products.Three types of attribute domains are used in this paper: discrete,tree,and numeric domains(Ryu,1999).A discrete domain contains discrete values,such as brand.A tree domain is whose elements are structured as a tree and its purpose is tofind the replacement products(Lee& Widmeyer,1998;Ryu).Fig.1displays an example of the tree domain for attribute‘CD/DVD option’of the notebook computer.Each branch of the tree indicates an alternative function or an attribute value of the product.For example, assume that a buyer wants to purchase a notebook computer with‘CD-R’.The replacement product can be a product with‘CD-ROM’,‘DVD-ROM’,or‘DVD-RAM’and the product with CD-ROM has a higher priority to purchase,J.Wang,C.-H.Dai/Expert Systems with Applications27(2004)593–607 594because both CD-R and CD-ROM are located in the same smallest subtree.The attribute with the numeric domain has numeric values,such as product weight,price,etc.Since the satisfaction of each buyer requirement may not be strictly either true or false,fuzzy set theory is used to measure the satisfaction degree of a product to each buyer requirement for three types of attribute domains.We will explain this in more details in Section 3.In addition,each numeric attribute is considered as a linguistic variable containing linguistic terms that can be modeled by fuzzy set theory.The linguistic terms can be used by the novice buyer,who is not familiar with the purchasing products,to express his requirements.This allows the novice buyer to express his requirements more naturally.The linguistic terms of a linguistic variable can be interpreted as specific fuzzy numbers.The fuzzy numbers have the usual trapezoidal shapes that are defined on the range over the domain of the corresponding numeric attribute.For example,for the attribute ‘weight’of the notebook computer,we can define it as a linguistic variable which has the term set Z {‘light’,‘medium’,‘heavy’}for the linguistic values of its domain that these terms can be characterized by membership functions (1.2,1.2,1.2,2.2),(1.5,2.5,2.5,3.2),and (2.8,3.5,3.5,3.5),respectively (see Fig.2).Similarly,the relative importance of product attributes also can be evaluated by linguistic terms;e.g.{‘very important’,‘rather important’,‘important’,‘less important’,‘unimportant’}.The basic concept of fuzzy set theory is introduced in Appendix A.3.Methodology for electronic shopping assistance This paper considers the electronic shopping assistance problem as a fuzzy constraint satisfaction problem (Dubois,Fargier,&Prade,1994).Each buyer requirement is considered as a constraint.Let X j be an attribute and r be a legal value within the attribute domain.Three types of constraints can be defined:ðGreater-than-or-equal-to constraint ÞX j R r(1)ðEqual-to constraint ÞX j Z r (2)ðLess-than-or-equal-to constraint ÞX j %r(3)The satisfaction degree of product P i to buyer requirement R j regarding attribute X j is defined as C (R j ,P i )2[0,1].In the following,we develop methods to measure the satisfaction degree of the buyer requirement for three domain types in Sections 3.1and 3.2.The lexicographic ordering approach used to generate the product-ranking list is presented in Section 3.3.The similarity analysis approach is developed in Section 3.4to estimate buyer requirements for the buyer with the self-guided shopping behavior.3.1.Modeling buyer requirements as constraints—discrete and tree domainsFor the attribute with the discrete or tree domains,only the ‘equal-to’constraint can be used.Let x ij be the value of attribute X j for product P i .The satisfaction degree of product P i regarding buyer requirement X j Z r for discrete domain can be defined:C ðX j Z r ;P i Þ)1;x ij Z r0;otherwise ((4)For example,if the buyer requirement for attribute ‘brand’of the notebook is ‘ACER’,then the satisfaction degree of the notebook computer with the brand ACER is equal to one;otherwise,it is equal to zero.For attribute X j with the tree domain,the satisfaction degree of product P i regarding buyer requirement X j Z r can be defined:C ðX j Z r ;P i ÞZ 1x ij Z r 1K dist ðu ;r Þd Max x ijZ u o u s r;8<:(5)where dist(u ,r )is the number of edges between r and the root node of the smallest sub-tree containing u and r ,and d Max is the depth of the tree;i.e.the maximum number of edges between the root node and the leaf node of the tree.For example,consider an example of the tree domain shown in Fig.1for attribute CD/DVD option of the notebook computer.Assume that a buyerdemandsFig.1.An example of the tree domain for the CD/DVD option of notebookcomputers.Fig.2.Membership functions for the linguistic terms of attribute ‘weight’.J.Wang,C.-H.Dai /Expert Systems with Applications 27(2004)593–607595a notebook computer with a DVD-ROM;i.e.X CD/DVD Z DVD-ROM.According to Eq.(5),the satisfaction degree of a notebook computer P1that has a CD-ROM can be computed:CðX CD=DVD Z DVD-ROM;P1ÞZ1K distðCD-ROM;DVD-ROMÞdZ13;where d Max Z3and dist(CD-ROM,DVD-ROM)Z2. Similarly,the satisfaction degree of a notebook computer P2that has a DVD-RAM is:CðX CD=DVD Z DVD-ROM;P2ÞZ 2 3 :From the tree domain of Fig.1,DVD-RAM is located at the same smallest subtree as DVD-ROM.Therefore, the product with DVD-RAM is more satisfactory than the product with CD-ROM for the buyer requirement X CD/DVD Z DVD-ROM.3.2.Modeling buyer requirements as constraints—numeric domainIn this paper,each numeric product attribute is considered as a linguistic variable whose values are expressed by linguistic terms and the membership functions of the linguistic terms are interpreted as specific fuzzy numbers.To calculate the satisfaction degree of a numeric product attribute to its buyer requirement,wefirstly convert both attribute value and the corresponding buyer require-ment into vector forms,called the product attribute vector and the buyer requirement vector,respectively.Then,the satisfaction degree can be computed as the similarity degree between these two vectors.The product attribute vector used to describe the numeric attribute value of a product is defined as follows.Definition.Product attribute vector.Letð~L1;~L2;.;~L qÞbe the ordered set of q fuzzy sets associated with the linguistic terms defined for numerical attribute X j2X and v ij be the attribute value of product P i2P for X j.The product attribute vector(u i1,u i2,.,u iq)regarding P i consists of q ordered elements and each element u ik,k2[1,q],is the membershipgrades of~L k;i.e.u ik Z m~Lk ðv ijÞ;where m~L kis the membershipfunction of~L k:Transforming a buyer requirement into a vector form is more complicate than a numeric attribute value,because three types of constraints(1)–(3)can be used and either crisp or linguistic buyer requirements may be given.The proposed approachfirstly transforms each numeric buyer requirement into a fuzzy set and then constructs the buyer requirement vector based on possibility theory(Dubois& Prade,1988).The membership function of fuzzy set~R for describing each type of numeric buyer requirement with a crisp value r regarding attribute X j can be defined asX j R r5m~RðxÞZ1;x R r0;otherwise((6) X j Z r5m~RðxÞZ1;x Z r0;otherwise((7) X j%r5m~RðxÞZ1;x%r0;otherwise((8)Similarly,fuzzy set~R for representing each linguistic buyer requirement can be defined based on the concept of fuzzy bounds(see Appendix A):X j R~rði:e:X2½~r;C NÞÞ5m~RðyÞZ supx%ym~vðxÞ(9) X j Z~r5m~RðyÞZ m~rðxÞ(10)X j%~rði:e:X2ðK N;~r Þ5m~RðyÞZ supx R ym~rðxÞ(11)Fig.3shows an example of the fuzzy sets for the linguistic buyer requirements‘product weight R medium’and‘product weight%medium’.The buyer requirement vector is defined based on possibility measure(Dubois&Prade,1988).Consider a parameter x whose values are restricted by a fuzzy set~A; whose possibility distribution is taken as equal to the membership function m~A:The possibility of the event x2~P to be true is defined as:Pðx2~PÞZ supuminðm~AðuÞ;m~PðuÞÞ(12)According to Eq.(12),we can define the buyer requirement vector as follows.Definition.Buyer requirement vector.Letð~L1;~L2;.;~L qÞbe the ordered set of q fuzzy sets associated with the linguistic terms defined for numerical attribute X j2X.Let~R be a fuzzy set that represents a buyer requirement for X j and y be a value restricted by~R:The buyer requirement vector (g1,g2,.,g q)for~R consists of q ordered elements andeachFig.3.Fuzzy sets for the linguistic buyer requirements:X weight R medium and X weight%medium.J.Wang,C.-H.Dai/Expert Systems with Applications27(2004)593–607 596element g k,k2[1,q],is the degree of~R that matches to~L k and is computed as:g k Z Pðy2~L kÞZ supx minðm~RðxÞ;m~LkðxÞÞ:(13)The satisfaction degree of a product attribute to the corresponding buyer requirement can be obtained by computing the similarity degree between the corresponding product attribute vector and the buyer requirement vector. Several similarity measures have been developed in the literature(Hong&Hwang,1994;Kwang,Song,&Lee, 1994;Pappis&Karacapilidis,1993;Wang,1997).We apply Wang’s approach in this paper,because it considers all elements of vectors and satisfies the necessary properties of similarity measures.Let G Z(g1,g2,.,g q)be the buyer requirement vector and U Z(u1,u2,.,u q)be the product attribute vector for a numeric attribute of a product.The satisfaction degree of the product to the buyer requirement regarding the attribute can be computed by the similarity degree between these two vectors(Wang,1997):CðG;UÞZ X qk Z1ð1K j g k K u k jÞq(14)Since some numeric attributes have the property of‘the-smaller-the-better’or‘the-larger-the-better’;e.g.the weight of the notebook computer.Before constructing the product attribute vectors or buyer requirement vectors,we have to transform the membership functions associated with these numeric attributes into the functions that demonstrate these properties.Letð~A1;~A2;.;~A qÞbe the ordered set of q fuzzy numbers representing linguistic terms defined for numerical attribute X j2X.The transformed membership function of the fuzzy number~L k associated with each linguistic term for the numeric attribute with the property the-smaller-the-better is written asm~Lk ðyÞZsup x R y m~AðxÞ;k2½1;q K1inf x%yð1K m~AðxÞÞ;k Z q((15) Similarly,the transformed membership function of thefuzzy number~L k for the numeric attribute with the property ‘the-bigger-the-better’is written asm~Lk ðyÞZsup x%y m~AðxÞ;k2½1;q K1inf x R yð1K m~AðxÞÞ;k Z q((16) For example,attribute weight for the notebook computerhas the property the-smaller-the-better,because buyers usually prefer to purchase a notebook computer with smaller weight.Fig.4displays the transformed membership functions~L1;~L2;and~L3associated with the linguistic terms light,medium,and heavy for attribute weight shown in Fig.2.For example,let X denote attribute weight and X Z2.0be the given buyer requirement.The above requirementcan be transformed into the buyer requirement vectorG Z(0.2, 1.0, 1.0),according to Fig.4and Eq.(13). Suppose that there are two products A and B in theelectronic store and their weights are equal to1.7and1.5.Both product weights can be transformed into the productattribute vectors U A Z(0.5,1.0,1.0)and U B Z(0.7,1.0, 1.0),respectively.According to Eq.(14),the satisfactiondegrees of both products to the buyer requirement can becomputed as follows:CðG;U AÞZðð1:0K j0:2K0:5jÞC1:0C1:0Þ=3Z0:90;CðG;U BÞZðð1:0K j0:2K0:7jÞC1:0C1:0Þ=3Z0:83: From the above result,product A is preferred.This is consistent with our intuition,because the‘equal-to’constraint is specified by the buyer and the weight product A is closer to the buyer requirement than product B.Consider another situation in which the buyerrequirement for attribute weight is specified as X%2.0(i.e.the-smaller-the-better).The buyer requirement canbe transformed into the buyer requirement vector(1.0,1.0,1.0)and the satisfaction degrees for products A andB are0.83and0.90,respectively.This means that product B is preferable to product A.Similar results can be obtained for linguistic buyerrequirements.For example,assume that the buyer require-ment is specified as X Z‘medium’.Its buyer requirementvector can be determined as(0.35, 1.0, 1.0)and thesatisfaction degrees of both products A and B are0.95and0.88,respectively.This means that product A is preferable toproduct B.The result obtained is also consistent with ourintuition,because the membership grade of the weight forproduct A is higher than product B according to themembership function of the linguistic term medium in Fig.2.3.3.Ranking products based on the lexicographicordering approachAfter the satisfaction degree of each product P i2P to every buyer requirement R j2R has beendetermined, Fig.4.Transformed membership functions of the linguistic terms for attribute‘weight’with the property‘the-smaller-the-better’.J.Wang,C.-H.Dai/Expert Systems with Applications27(2004)593–607597the lexicographic ordering algorithm adopted from Ryu(1999)is used to generate ranking orders of all products toassist buyers infinding desirable products.The basic idea of the original lexicographic orderingapproach isfirst to rank the attributes and then to select theproduct rated highest on the highest-ranked attribute.If atie occurs,the next most important attribute is used.Itsmajor disadvantage is that there is no trade-off amongdifferent product attributes.In other words,if a product isbetter than another product in the comparison against themost important product attribute,then the former is betterthan latter,even though the former is far worse than thelatter for all other attributes.Ryu(1999)applied theconcept of indifference threshold(Roy&Vincke,1984)toovercome this disadvantage.The indifference threshold r jis used to discriminate between indifference of twoproducts for every attribute X j2X.If the difference between these products does not exceed r j,then it is notconsidered significant and both products are indifferent forattribute X j.Therefore,if a product is better than anotherproduct regarding an attribute only if the differencebetween them is larger than the indifference threshold.For example,the indifference threshold for the weight ofnotebook computer can be set to0.15kg,because buyersusually cannot distinguish the weights of different note-book computers within this range.Let q i Z(q i1,q i2,.,q in)be a vector,called the product compatibility vector,which describes the suitability of product P i2P to the set R of buyer requirements,where q ij is the satisfaction degree of product P i to buyer requirement R j2R.Let r j be the indifference threshold for attributes X j. The modified lexicographic ordering algorithm is described as follows.Denote:P:set of all products being evaluated;m:the number of products;n:the number of product attribute;Lexicographic ordering algorithmInput:q:the set q Z{q1,q2,.,q m}of product compatibilityvectors;W:the set of ordered product attributes that are rankedaccording to their importance;r:the set r Z{r1,r2,.,r n}of indifference thresholds;Output:p h:ordered sets of products;Procedure:set p)P and h)1;repeat until p Z fp h)p;W0)W;repeat until j p h j Z1or W0Z f/*j†j:cardinality of aset*/Select the most important attribute X jÃfrom W0;For two products P i,P k2p h,if q ijÃK q kjÃO r jÃ;then remove P k from p h:Remove X jÃfrom W0;endp)p–p h;h)h C1;endend procedureAccording to the above algorithm,the products that are under consideration will be ranked in the ordered sets of products.Product P i is better than another product P k,if and only if there exist p a and p b with a!b,such that P i2p a and P k2p b.The indifference threshold r j for each attributeX j2X can be obtained from the inputs of buyers or the default system setting by sellers.Since the algorithm is performed on the scale of satisfaction degree,the indiffer-ence thresholds of all attributes are transformed into the values on the scale of membership grade within[0,1].For example,the indifference threshold for the weight of notebook computer can be set to0.05that is about 0.15kg.The algorithm is illustrated with the following example.Example.A buyer intends to make a purchasing decision among three products P1,P2,P3with only two attributes X1, X2and X1is more important than X2.Assume that the product compatibility vectors regarding the three products are computed as q1Z(0.4,0.3),q2Z(0.5,0.2),and q3Z (0.6,0.1).The indifference thresholds for two attributes are set to r1Z0.12and r2Z0.05,ing the above data,the algorithm is demonstrated as follows:Set p){P1,P2,P3}and h)1;Iteration1:Set p1){P1,P2,P3}and W0){X1,X2};Enter the inner loop until the termination conditionhas been met;Set j*)1,because X1is more important than X2;Remove P1from p1,because P1is worse than P3regarding X1;i.e.p1){P2,P3}.Remove X1from W0;Set j*)2;Remove P3from p1,because P3is worse than P2regarding X2;i.e.p1){P2};Remove X2from W0;The termination condition is satisfied and ends theinner loop;p){P1,P3};h)2;Iteration2:Set p2){P1,P3}and W0){X1,X2};Enter the inner loop until the termination conditionhas been met;Set j*)1;None of them in p2can be removed;Remove X1from W0;Set j*)2;Remove P1from p2;i.e.p2){P3};Remove X1from W0;J.Wang,C.-H.Dai/Expert Systems with Applications27(2004)593–607 598。

Performance appraisal and employee satisfactionAbstract: The performance appraisal is often referred to as performance appraisal or "performance" is for the enterprise work undertaken by each employee, qualitative and quantitative application of scientific methods, the actual effect on staff behavior and their contribution to the enterprise or value evaluation.Performance appraisal as an effective business management tools, in the enterprise management plays a very important role, is the core of human resource management.This article on the current performance appraisal of the problems to do a detailed analysis.To tackle the problem, the paper proposes the performance evaluation of all angles from the control to ensure effective performance appraisal in place, and ultimately play the role of human resource management.Keywords: Performance Evaluation with analysis of the proposed21st century is the era of knowledge economy, as economic competition intensifies, it is increasingly recognized that human resources are the current era of economic development of the first resource.As the human resources management in the development of Chinese enterprises become more sophisticated, performance management, human resources management as an important component of the position within the enterprise is also more important.Human resource management performance appraisal is one of the core issue is to protect and promote the orderly operation of the internal management mechanism, the management objectives of the enterprise must be carried out by a management behavior.Organizational behavior United States where scientists Yuehan Yi Las its view that performance assessment can achieve the purpose of the following eight areas: staff promotion, demotion, transfer and separation of the assessment; organization employee performance evaluation feedback; employees and team to assess the contribution of the organization; to provide the basis for employee compensation decisions; for the recruitment selection and assessment of the work allocation decisions; understand the staff and team training and education needs; understanding of staff and team training and education needs; the work plan, budget and human resources planning assessments to provide information.Employee performance appraisal is an effective means of business management is the primary means of business management in the core of irreplaceable.However, there are a lot of business performance evaluation and business development strategy for the phase out of line, business performance evaluation system is only an empty shell it impossible to achieve the purpose of staff appraisal, and even counterproductive, leading to brain drain.Therefore, the work of the enterprise's performance appraisal analysis to identify problems and solve these problems become imperative to work.1Current Problems and Performance Assessment Analysis1.1 pairs of inadequate understanding of performance appraisal(1) That the performance appraisal is only human resources matter.Many enterprises believe that the performance appraisal is performance management content, and performance management is one of the functions of human resource management, so that HR performance evaluation is only a matter.Corporateexecutives only the instructions on the implementation of performance appraisal is not specifically guidance; Human Resources functions in communication with the other how to improve the performance appraisal can not be actively cooperate.(2) Insufficient understanding of the objectives of performance appraisal.Many companies now emphasize the introduction of advanced assessment tools, and leadership that the assessment is Jiangyoufalie, the ultimate goal of performance appraisal is not a clear understanding.The fundamental purpose of performance appraisal is to promote the effectiveness and efficiency, improve performance; performance evaluation is to improve the fundamental purpose is to work in accordance with the provisions of assessing whether the staff to complete tasks.The quality is not the purpose of examination results, but to analyze the reasons.(3) That the performance evaluation exist independently.Although performance appraisal is an essential business management core, but not to independent existence, it needs as a basis for other related work.The final appraisal is just a part of, and this assessment must be based on a few to be effective based on: reasonable performance goals, clear performance standards, performance counseling and objective record of performance, performance improvement and employee skills development.Only on the basis of these work, performance evaluation will be objective and fair in order for staff to accept, but also a greater practical significance.1.2 The purpose of performance appraisal is not clear(1) Goal setting fuzzy, set during the lack of effective control.Work schedule has set a target column, has asked each of the assessment system must have clear objectives.If the enterprises to implement performance appraisal, then they would know exactly why the implementation of performance appraisal.However, the actual implementation point of view, the current performance appraisal of the purpose of many companies is not clear, many companies do not have a clear purpose of performance appraisal, and sometimes even for assessment and evaluation, business evaluation appraisal side by side and not fully clear understanding of the performance appraisal just a management tool in itself is not the purpose of management. Most enterprises in the work schedule is basically a column filled goal setting are "complete", but this does not reflect the work "completed" the specific conditions, so that assessment can not start.(2) The purpose of the enterprise performance appraisal is not enough understanding of the phenomenon is that many companies have problems.Many managers will be the management and performance appraisal as a means of controlling employees that the purpose of performance appraisal is to enable employees in accordance with the arrangements and willingness of managers to do work.Therefore, managers will be a way to contain the performance appraisal staff, to establish their own credibility and to show their authority, the performance appraisal of staff performance problems as challenges, criticism and punishment according to the staff that the psychological staff performance appraisal a great deal of pressure, creating a bad impact, so that employees feel that performance appraisal for managers to control their instruments and tools, it is equivalent to the so-called fault-finding performance appraisal.Thus, employees will have reverse psychology to increase thefear, it will naturally produce resentment on the performance appraisal system, and eventually failure of the implementation of performance appraisal.(3) The purpose of performance appraisal can be divided into five categories: First, as a promotion, dismissal, and adjust the position of the basis; Second, for determining the salary and bonus basis; three, as the potential basis for the development and education and training; four, as adjusted personnel policy, based on incentives; five, examination results for the production, procurement, marketing, research and development, finance and other departments to develop work plans and decision-making reference.Only the clear purpose of performance appraisal, the performance assessment may focus on this goal was well underway.1.3Performance evaluation standard design unscientific(1) Performance appraisal standard fuzzy, lack of performance as a standard, standards and relevance of the work is not strong, operational poor or too subjective, too single, and standards are not quantified and so on.Work standards, only a few words of reviews, not an objective scoring scale so that the evaluators are free to givea score or examination results.(2) Employee performance appraisal, the result difficult to judge objectively, the subjective understanding of the different results of the evaluation bias.Result, the standard will have a different measure of more or less favorable.Some assessment were too high, often show the work of the staff was disappointed in the assessment, they will underestimate the evaluation of staff should be.On the contrary, some assessment of employees who think the best is simply not exist, the worst is hard to find employees, so employees are often used to be classified as middle class.Therefore, employees do not want to accept the examination results.(3) Lack of clear performance goals.Business employees do not know what their requirements are not clear what extent do considered as well, therefore, their performance is difficult to get corporate approval. Some companies are just a form of performance appraisal, there is no real content, performance appraisal every year, although in practice, but every year is "nowhere near", "fly."So that the performance results lose their meaning, no longer has objectivity, comparability and effectiveness.1.4 Performance Evaluation Index System flawed(1) Performance appraisal system design is not realistic.As the scale of the enterprise management level and uneven, business performance evaluation and management-level inputs also varied.Some enterprises have developed their own corporate management performance targets, but because of performance management in theory at this stage is still lack of scientific and practical methods, or because of corporate performance management and evaluation committee members lack of experience, so the decomposition is not appropriate performance indicators, assessment purpose is not clear, the principles of confusion and contradictory assessment issues, which planted the hidden performance targets difficult to complete.(2) Lack of scientific performance appraisal system design, practicality.Management performance evaluation system to evaluate the work of the foundation and core, and many enterprises did not use fully understand the importance of performance evaluation, full flow in one form, the performanceassessment and evaluation in order.The contents of the appraisal, the project settings and set the weight so often show no correlation and randomness, the will and personal likes and dislikes obvious.At the same time, many enterprises performance evaluation standards are too vague and difficult to accurately quantify less practical, easily lead to incomplete, non-objective and impartial judgments, so that the performance results difficult to be convinced.2 solve the problems proposed performance appraisal2.1 Establish the scientific concept of performance(1) Leadership need to clear the great role of performance appraisal.Performance evaluation can not only enhance the competitiveness, but also improve employee productivity, performance evaluation is good or bad determines the quality of enterprise management, and its function more and more prominent.First of all, improve employee performance appraisal is an important basis for work and training.Through regular assessment, employees can clearly see in what areas their own has increased, in what areas need to continue strong, the right to own a position.Meanwhile, the performance appraisal is to provide a different level of employees say what platform to those mediocre and lazy to expose the bad behavior, optimize human resources; more staff in the mirror and reinforce the correct behavior and reward employees effective basis. Nowadays, many enterprises of the old ideas, old practices remain unchanged, human resources and the environment can not be optimistic, to establish an advanced, highly effective performance appraisal system is not easy, especially, corporate leadership must establish the scientific concept of performance, a reasonable performance evaluation system, otherwise, it is difficult to achieve the desired results.(2) Increase the levels of staff training and publicity.Performance appraisal is the basis for promotion and training.Through regular assessment, the employees themselves can understand what has been improved, in which there is still insufficient.Performance appraisal system, although only a writing system, but in the specific needs of the implementation process at all levels of managers with the skills, performance appraisal, such as determining the objectives of the skills, interview skills, evaluation skills, which require training. Through training, so that managers work to develop the items and objectives, understanding staff performance appraisal methods, processes and responsibilities, improve communication skills, to develop performance improvement plans, effective implementation of the counseling.Through advocacy, the staff performance appraisal system, part of the composition and the organic link between well aware of, and implementation of employee performance appraisal program clear understanding of the inner link.Eventually through advocacy and training reflect human management of the performance assessment to be a consensus, thus trying to explore the enterprise contains abundant human resources, to achieve the intended purpose of assessment.2.2 The establishment of a reasonable performance evaluation system(1) Set goals.Enterprise should have a clear work objectives, to start work around this goal and towards the goal to guide the staff development.In determining the performance goals, the need for performance counseling session, the departmentmanager employee goals to continue to communicate with the process, do everything to maintain close contact with employees, continue to give staff support on the road ahead for its removal obstacles.That is the goal of staff together with the company, as far as possible to each and every staff, especially managers, are the work of the company's goal to achieve, together in the same direction, should individual performance improved organizational performance improvement and the combination of the vital interests of employees, the establishment of incentive systems.(2) Rreference method.Many methods of performance appraisal, the enterprise according to the actual situation of their own assessment methods to learn from others.However, no reference is copied.Science, advanced assessment methods, such as the Balanced Scorecard BSC, costing ABC, integrated performance management, IPM, are very worth learning methods.(3) Systematic evaluation cycle.Routinely with the monthly, quarterly and annual examination closely linked.To routinely based, the normal performance appraisal results as the work of employees is one important basis for evaluation.To give full play to goal-oriented performance appraisal system for managing the effect of the annual general appraisal, performance evaluation should be based on reasonable providing encouragement, more importantly, the results for the staff and the ability to work, the proposal should receive training to its to effectively improve their ability to work with development potential.2.3 And the standard performance index optimizationDesign a scientific and reasonable performance index and standard system, the fully reflect the merits of a business management performance is critical.Therefore, assessment of enterprise performance indicators and standards to follow the scientific, systematic, importance, comparable, workable principles, will be independent of individual indicators, according to the organic combination of internal relations together can build a real, scientific, fully reflect the situation of business management performance index and standard system.Establish the right of each performance measure and standard, we need to determine the strategic direction of performance appraisal, assessment methods to strengthen the supervision of the implementation process and final sound of each job objective and reasonable analysis.But also the results of the analysis develop a performance index of each post and standards, the implementation process should pay attention to "two with":(1)Performance evaluation and quality assessment combined.Improve the performance appraisal performance assessment in addition to outside content; there should be quality of the assessment. Performance evaluation can effectively stimulate the employees to complete their duties as required; quality assessment is to promote staff to enhance the overall quality of personal attention and encourage teamwork. A correlation between the role of promotion, so that both businesses and employees have been harmonious development.(2) Focus on the combination of examination and general assessment.Enterprises to settle down after the assessment indicators, but also the establishment in the overall index in the key indicators and general indicators.The impact of large, difficult, related to the business development and strategic objectives, reflecting the importantfunctions of the position indicators, evaluation indicators should be identified as a priority; to little effect, the difficulty small, short period of time to complete, the development of enterprises is not too much contact of the index, to determine the general assessment indicators.Key assessment indicators and general indicators of effective integration of assessment, prioritized, can play a better assessment of its role.2.4 The integrated use of assessment results, effective feedbackWhether the performance appraisal results in a reasonable manner, the effect of the performance appraisal is a vital link.Appropriate use of evaluation results, the implementation of performance appraisal would have a very large role in promoting the role of performance appraisal is also a positive; the other hand, the work will be the effectiveness of performance appraisal would have a huge impact.Therefore, the emphasis on the integrated use of performance evaluation results are very important and necessary.(1)The establishment of the principle of open examination results.Enterprise performance evaluation standards, evaluation procedures and evaluation of the results should be clearly defined, and all staff to encourage employees to participate in public, and in the assessment of these provisions should be strictly observed, so the assessment process transparent and open.In order to make performance appraisal staff have a sense of trust in order to maintain the performance results on the understanding and acceptance.Meanwhile, the results of the assessment must be timely feedback to me, let truly understand and identify with their work the previous period, the two sides can discuss the basis of improved performance possible.In the performance feedback interview, should be noted that two-way communication, to ask less about the problem both diagnosis and counseling, not only talking about the past, but should be based on the future.(2)Promptly after the examination results to communication with staff.The review is not conducted by the evaluation of the main one, which is the main examination, assessment objects, assessment criteria, assessment methods, assessment procedures and other components of the interrelated whole.In the performance evaluation, to follow the principles of communication, and engage in patriarchal system, which allows employees to ask questions, explain the problem and the opportunity to make recommendations, and staff equal to communicate with each other and let everyone participate in the evaluation activities.If there is no performance evaluation indicators for assessment and evaluation based on the specific content of such instructions to staff on the full, and do not give employees the opportunity to participate, it may lead to staff on the assessment results are not ideal, discontented, it is necessary to establish two-way communication mechanism managers and staff work together to develop performance indicators to assess the situation on the completion of analysis and propose an improved method, in order to make people think that performance appraisal is open, fair, employees will be on the evaluation results to understand, accept and improve their own inadequacies.3 ConclusionEnterprise in the implementation of China's current performance appraisal occurswhen different problems are inevitable, it is important to think in the process, find the problem, and a reasonable analysis of the problem and find ways of targeted measures to address these issues.Only a clear analysis of the root of the problem, according to the actual situation of targeted, timely and accurate use of appropriate methods and technical means to do it well performance evaluation, performance appraisal can give full play to enhance the core competitiveness of enterprises in the great role in promoting more effective achievement of corporate strategic objectives, to promote continuous healthy and sustainable development.。