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Combining classifiers of pesticides toxicity through aneuro-fuzzy approachEmilio Benfenati1, Paolo Mazzatorta1, Daniel Neagu2, and Giuseppina Gini21 Istituto di Ricerche Farmacologiche "Mario Negri" Milano,Via Eritrea, 62, 20157 Milano, Italy{Benfenati, Mazzatorta}@ marionegri.it2 Dipartimento di Elettronica e Informazione, Politecnico di Milano,Piazza L. da Vinci 32, 20133 Milano, ItalyNeagu@fusberta.elet.polimi.it, Gini@elet.polimi.ithttp://airlab.elet.polimi.it/imagetoxAbstract. The increasing amount and complexity of data in toxicity predictioncalls for new approaches based on hybrid intelligent methods for mining thedata. This focus is required even more in the context of increasing number ofdifferent classifiers applied in toxicity prediction. Consequently, there exist aneed to develop tools to integrate various approaches. The goal of this researchis to apply neuro-fuzzy networks to provide an improvement in combining theresults of five classifiers applied in toxicity of pesticides. Nevertheless, fuzzyrules extracted from the trained developed networks can be used to performuseful comparisons between the performances of the involved classifiers. Ourresults suggest that the neuro-fuzzy approach of combining classifiers has thepotential to significantly improve common classification methods for the use intoxicity of pesticides characterization, and knowledge discovery.1 IntroductionQuantitative structure–activity relationships (QSARs) correlate chemical structure to a wide variety of physical, chemical, biological (including biomedical, toxicological, ecotoxicological) and technological (glass transition temperatures of polymers, critical micelle concentrations of surfactants, rubber vulcanization rates) properties. Suitable correlations, once established and validated, can be used to predict properties for compounds as yet unmeasured or even unknown.Classification systems for QSAR studies are quite usual for carcinogenicity [9], because in this case carcinogenicity classes are defined by regulatory bodies such as IARC and EPA. For ecotoxicity, most of the QSAR models are regressions, referring to the dose giving the toxic effect in 50% of the animals (for instance LC50: lethal concentration for 50% of the test animals). This dose is a continuous value and regression seems the most appropriate algorithm. However, classification affords some advantages. Indeed, i) the regulatory values are indicated as toxicity classes and ii) classification can allow a better management of noisy data. For this reason we investigated classification in the past [7], [8], [9] and also in this study. No generalrule exists to define an approach suitable to solve a specific classification problem. In several cases, a selection of descriptors is the only essential condition to develop a general system. The next step consists in defining the best computational method to develop robust structure–activity models.Artificial neural networks (ANNs) represent an excellent tool that have been used to develop a wide range of real-world applications, especially when traditional solving methods fail [3]. They exhibit advantages such as ideal learning ability from data, classification capabilities and generalization, computationally fastness once trained due to parallel processing, and noise tolerance. The major shortcoming of neural networks is represented by their low degree of human comprehensibility. More transparency is offered by fuzzy neural networks FNN [14], [16], [18], which represent a paradigm combining the comprehensibility and capabilities of fuzzy reasoning to handle uncertainty, and the capabilities to learn from examples.The paper is organized as follows. Section 2 briefly presents the aspects of data preparation, based on chemical descriptors, some of the most common classification techniques and shows how they behave for toxicology modeling, with a emphasis to pesticides task. Section 3 proposes the neuro-fuzzy approach in order to manage the integration of all the studied classifiers, based on the structure developed as FNN Implicit Knowledge Module (IKM) of the hybrid intelligent system NIKE (Neural explicit&Implicit Knowledge inference system [17]). Preliminary results indicate that combination of several classifiers may lead to the improved performance [5], [11], [12]. The extracted fuzzy rules give new insights about the applicability domain of the implied classifiers. Conclusions of the paper are summarized in the last section.2 Materials and Methods2.1 Data setFor this paper a data set constituted of 57 common organophosphorous compounds has been investigated. The main objective is to propose a good benchmark for the classification studies developed in this area. The toxicity values are the result of a wide bibliographic research mainly from “the Pesticide Manual”, ECOTOX database system, RTECS and HSDB [1]. An important problem that we faced is connected with the variability that the toxicity data presents [2]. Indeed, it is possible to find different fonts showing for the same compound and the same end–point LC50 different for about two orders of magnitude. Such variability is due to different factors, as the different individual reactions of organisms tested, the different laboratory procedures, or is due to different experimental conditions or accidental errors.The toxicity value was expressed using the form Log10 (1/LC50). Then the values were scaled in the interval [-1..1]. Four classes were defined: Class 1 [-1..-0.5), Class 2 [-0.5..0), Class 3 [0..0.5), Class 4 [0.5..1] (Table 2).2.2 DescriptorsA set of about 150 descriptors were calculated by different software: Hyperchem 5.01, CODESSA 2.2.12, Pallas 2.13. They are split into six categories: Constitutional (34 descriptors), Geometrical (14), Topological (38), Electrostatic (57), Quantum–chemicals (6), and Physico–chemical (4). In order to obtain a good model, a selection of the variables, which better describe the molecules, is necessary. There is the risk that some descriptors does not add information, and increase the noise, making more complex the result analysis. Furthermore, using a relatively low number of variables, the risk of overfitting is reduced. The descriptors selection (table 1) was obtained by Principal Components Analysis (PCA), using SCAN4:Table 1. Names of the chemical descriptors involved in the classification task.Cat. Cod.Moment of inertia A G D1Relative number of N atoms C D2Binding energy (Kcal/mol) Q D3DPSA-3 Difference in CPSAs (PPSA3-PNSA3) [Zefirov’s PC] E D4Max partial charge (Qmax) [Zefirov’s PC] E D5ZX Shadow / ZX Rectangle G D6Number of atoms C D7Moment of inertia C G D8PNSA-3 Atomic charge weighted PNSA [Zefirov’s PC] E D9HOMO (eV) E D10LUMO (eV) Q D11Kier&Hall index (order 3) T D122.3 Classification algorithmsThe classification algorithms used for this work are five: LDA (Linear Discriminant Analysis), RDA (Regularized Discriminant Analysis), SIMCA (Soft Independent Modeling of Class Analogy), KNN (K Nearest Neighbors classification), CART (Classification And Regression Tree). The first four are parametric statistical systems based on the Fisher’s discriminant analysis, the fifth and sixth are not parametrical statistical methods, the last one is a classification tree.LDA: the Fischer’s linear discrimination is an empirical method based on p–dimensional vectors of attributes. Thus the separation between classes occurs by an hyperplane, which divides the p–dimensional space of attributes.RDA: The variations introduced in this model have the aim to obviate the principal problems that afflict both the linear and quadratic discrimination. The regulation more efficient was carried out by Friedman, who proposed a compromise between the two previous techniques using a biparametrical method for the estimation (λ and γ).1 Hypercube Inc., Gainsville, Florida, USA2 SemiChem Inc., Shawnee, Kansas, USA3 CompuDrug; Budapest, Hungary4 SCAN (Software for Chemometric Analysis) v.1.1, from Minitab: SIMCA: the model is one of the first used in chemometry for modeling classes and, contrarily to the techniques before described, is not parametrical. The idea is to consider separately each class and to look for a representation using the principal components. An object is assigned to a class on the basis of the residual distance, rsd 2, that it has from the model which represent the class itself:()22ˆigj igj igj x xr −=, )(22j j igjM p r rsd −=∑ (1)where x igj = co –ordinates of the object’s projections on the inner space of the mathematical model for the class, x igj = object’s co –ordinates, p=number of variables, M j = number of the principal components significant for the j class.KNN: this technique classifies each record in a data set based on a combination of the classes of the k record(s) most similar to it in a historical data set (where k = 1). CART is a tree –shaped structure that represents sets of decisions. These decisions generate rules for the classification of a data set. CART provides a set of rules that can be applied to a new (unclassified) data set to predict which records will have a given outcome. It segments a data set by creating two –way splits.The classification obtained using these algorithms is shown in Table 2.2.4 ValidationThe more common methods for validation are: i) Leave –one –out (LOO); ii) Leave –more –out (LMO); iii) Train & Test; iv) Bootstrap. We used LOO, since it is considered the best working on data set of small dimension [10]. According to LOO, given n objects, n models are computed. For each model, the training set consists of n –1 objects and the evaluation set consists of the object left. To estimate the predictive ability, we considered the gap between the experimental (fitting) and the predicted value (cross –validation) for the n objects left, one by one, out from the model.Table 2. True class and class assigned by the algorithms for each compound 5.True Class CART LDA KNN SIMCARDAAnilofos 2 2 2 1 2 2 Chlorpyrifos1 2 2 1 2 2 Chlorpyryfos-methyl 2 2 2 1 2 2 Isazofos 1 1 1 2 1 1 Phosalone 2 2 2 2 2 2 Profenofos 1 2 2 1 2 2 Prothiofos 2 2 2 2 2 2 Azamethiphos 2 2 2 1 4 2 Azinphos methyl 1 1 1 2 1 1 Diazinon 3 3 1 1 4 1 Phosmet2 2 2 1 2 2 Pirimiphos ethyl 1 1 1 1 1 1 Pirimiphos methyl2312115 The 40 molecules with a blank background were used to train the neuro-fuzzy classifier.Pyrazophos 2 2 1 4 2 1Quinalphos 1 1 1 2 1 1Azinphos-ethyl 1 1 1 1 2 1Etrimfos 1 1 1 3 3 1Fosthiazate 4 2 2 2 4 2Methidathion 1 1 1 1 1 1Piperophos 3 3 3 2 2 3Tebupirimfos 4 1 1 3 4 1Triazophos 1 1 1 2 1 1Dichlorvos 2 4 2 2 2 2Disulfoton 3 3 3 1 3 3Ethephon 4 4 4 4 4 4Fenamiphos 1 1 3 2 1 1Fenthion 2 2 3 2 2 3Fonofos 1 1 3 2 1 3Glyphosate 4 4 4 4 4 4Isofenphos (isophenphos) 3 3 3 1 3 3Methamidophos 4 4 4 3 4 4Omethoate 3 3 3 3 3 3Oxydemeton-methyl 3 3 3 3 3 3Parathion ethyl (parathion) 2 2 2 3 1 3Parathion methyl 3 3 3 3 3 3Phoxim 2 2 1 1 1 1Sulfotep 1 1 3 2 2 2Tribufos 2 2 2 2 2 2Trichlorfon 2 2 2 1 2 4Acephate 4 4 1 3 4 4Cadusafos 2 2 3 3 2 2Chlorethoxyfos 2 2 2 3 2 2Demeton-S-methyl 3 3 3 3 3 3Dimethoate 3 3 1 1 3 3Edifenphos 2 2 3 1 2 2EPN 2 2 2 2 2 2Ethion 2 2 2 2 2 2Ethoprophos 3 3 3 2 2 3Fenitrothion 3 2 3 3 3 3Formothion 3 3 2 3 3 3Methacrifos 2 2 2 2 2 3Phorate 1 1 3 2 1 3Propetamphos 3 3 3 4 2 3Sulprofos 3 3 3 2 3 3Temephos 3 3 2 1 3 2Terbufos 1 1 3 2 3 3Thiometon 3 3 3 3 3 33.1 The neuro-fuzzy combination of the classifiers3.2 Motivations and architectureCombining multiple classifiers could be considered as a direction for the development of highly reliable pattern recognition systems, coming from the hybrid intelligent systems approach. Combination of several classifiers may result in improved performances [4], [5]. The necessity of combining multiple classifiers is arising from the main demand of increasing quality and reliability of the final models. There are different classification algorithms in almost all the current pattern recognition application areas, each one having certain degrees of success, but none of them beingas good as expected in applications. The combination technique we propose for the toxicity classification is a neuro-fuzzy gating of the implied classifiers, trained against the correct data. This approach allows multiple classifiers to work together.For this task, the hybrid intelligent system NIKE was used, in order to automate the processes involved, from the data representation for toxicity measurements, to the prediction of toxicity for given new input. It also suggests how the fuzzy inference produced the result, when required [17], based on the effect measure method to combine the weights between the layers of the network in order to select the strongest input-output dependencies [6]. Consequently, for NIKE, we defined the implicit knowledge as the knowledge acquired by neural/neuro-fuzzy nets.Fig. 1. Implicit Knowledge Module implemented as FNN2.The IKM-FNN is implemented as a multilayered neural structure with an input layer, establishing the inputs to perform the membership degrees of the current values, a fully connected three-layered FNN2 [16], and a defuzzification layer [17] (fig.1). The weights of the connections between layer 1 and layer 2 are set to one. A linguistic variable X i is described by m i fuzzy sets, A ij, having the degrees of membership performed by the functions µij(x i), j=1,2,...,m i, i=1,2,..,p., (in our case, p=5, all m i=4, on the classes of the prediction result of the classifiers, as inputs, and on the classes of the toxicity values, as the output y defuz). The layers 1 and 5 are used in the fuzzification process in the training and prediction steps, and the layers 2-4 are organized as a feedforward network to represent the implicit rules through FNN training [15][19]. 3.2 ResultsSince NIKE modules process only data scaled into the interval [0..1], every class was represented by the centroid of each of the four classes in which the available domain was split: 0.135 (class 1), 0.375 (class 2), 0.625 (class 3), and 0.875 (class 4). The inputs and the output followed a trapezoidal (de)fuzzification (fig. 2): VeryLow (0-0.25), Low (0.25-0.5), Medium (0.5-0.75), High (0.75-1).The neuro-fuzzy network was trained on a training set of 40 objects (70% of the entire set, as depicted in Table 2). The training set was used for the adjustment of the connections of the neural and neuro-fuzzy networks with backpropagation (traingdx) algorithm; traingdx is a network training function that updates weight and bias values according to gradient descent momentum and an adaptive learning rate. The neuro-fuzzy network was a multi-layered structure with the 5x4 above described fuzzy inputs and 4 fuzzy output neurons, the toxicity class linguistic variable (fig. 2.a). The number of hidden neurons parameterized the FNN. After different models (5 to 50 hidden units), a medium number of hidden units is desirable and had the same best results: IKM-FNN with 10, 12 and 19 neurons (fig. 3).(a) (b)Fig. 2. NIKE: (a)The fuzzy terms of the generic linguistic variable Class; (b) the FNN model. Table 3. Performances of the classification algorithms computed.NER% fitting NER%validation DescriptorsLDA 64.91 61.40 D1,D2, D3, D4RDA 84.21 71.93 D1, D2, D3, D4, D6, D7, D8, D11, D12, D13 SIMCA 92.98 77.19 D1, D2, D3, D4, D5, D6, D7, D8, D10, D11, D12 KNN - 61.40 D1, D12CART 85.96 77.19 D1, D2, D3, D4, D5, D9Table 4. Confusion matrix of the neuro-fuzzy combination of classifiers.N° of objectsAssigned Class1 2 3 41 132 15True Class2 20 203 1 15 164 6 6Table 5. True class and class assigned by all the classifiers for each compound wrong predicted by the neuro-fuzzy combination of classifiers.True Class CART LDA KNN SIMCA RDA FNN Chlorpyrifos 1 2 2 1 2 2 2Profenofos 1 2 2 1 2 2 2Fenitrothion 3 2 3 3 3 3 2(a)(b)(c)(d)(e)(f)Fig. 3. The results of training FNNs: (a) 3-5 errors, the best are FNN10H, FNN12H and FNN19H; (b) the chosen model, FNN10H, against the SIMCA results and the real ones; (c) the bad fuzzy inference prediction for 2 cases in class 1 (Chlorpyrifos and Profenofos); (d) the bad fuzzy inference prediction for the case in class 3 (Fenitrothion); two samples of good prediction for test cases: (e) a class 1 sample (Phorate); (f) a class 2 sample (Edinfenphos).A momentum term of 0.95 was used (to prevent too many oscillations of the error function). The nets were trained up to 5000 epochs, giving an error about 0.015. The recognition error for the above models is 5.26% (table 4, 5, fig. 3).The confusion matrix shows the ability in prediction of our approach. Looking of Table 3, we notice that the best performance was obtained by SIMCA, which could correctly classify almost 93% of the molecules. This encouraging result was obtained with whole data set involved in developing the model. If we take a look to the NER% validated with LOO, we can notice that we loss a lot of the reliability of the model when we predict the toxicity of an external object. Such a behavior proves the ability in modeling of these algorithms, but shows also their incapacity in generalization. The neuro-fuzzy approach seems to overcome this problem, succeeding in voting for the best opinion and underling all the considered classification algorithms (fig. 3).3.3 Interpreting the results of the neuro-fuzzy combination of the classifiers The most relevant fuzzy rules were extracted from the IKM-FNN structures using Effect Measure Method [6][13]. Finally, after deleting the contradictory rules, the next list of the most trusty fuzzy rules were considered for the chosen net IKM-FNN10H: IF CarFit1 is:VeryLow THEN class is:High (39.22%)IF CarFit1 is:Low THEN class is:High (82.30%)IF CarFit1 is:Medium THEN class is:High (48.74%)IF CarFit1 is:High THEN class is:High (39.04%)IF SimFit1 is:VeryLow THEN class is:Medium (61.25%)IF SimFit1 is:Low THEN class is:Medium (36.04%)IF SimFit1 is:High THEN class is:Medium (43.72%)IF RdaFit1 is:VeryLow THEN class is:Low (75.65%)IF RdaFit1 is:Low THEN class is:Low (100.00%)IF RdaFit1 is:High THEN class is:High (76.39%)Three types of fuzzy rules were obtained: some could be grouped by the same output, or by having the same fuzzy term in the premise and conclusion, and, finally, rules with mixed terms in premises and conclusion parts. From the first two groups of fuzzy rules (italics), we could conclude that, the opinion of the entry classifier is not important for the given output. More precisely, CART prediction for High values of toxicity (class 4) is better to not be taken in consideration.IF (CarFit1 is:VeryLow) OR (CarFit1 is:Low) OR (CarFit1 is:Medium) OR (CarFit1 is:High) THEN class is:HighSimilarly, SIMCA outputs are not so important for predicting class 3 (Medium toxicity: the second group of fuzzy rules). From the second last group of rules, we could find which is the best classifier from the involved systems. In our case, in order to predict class 2 (Low toxicity) is better to consider the opinion coming from RDA. The same opinion is very important for predicting the class 4 (High toxicity) cases too.ConclusionsClassification of the toxicity requires a high degree of experience from computational chemistry experts. Several approaches were described to generate suitable computer-based classifiers for the considered patterns. We investigated five different classifiers and a neuro-fuzzy correlation of them, to organize and classify toxicity data sets. Our approach shown an improved behaviour as a combination of classifiers. Some results viewing fuzzy rules extraction, as well as the possibility to interpret particular inferences suggest that the Neuro-Fuzzy approach has the potential to significantly improve common classification methods for the use in toxicity characterization. AcknowledgmentThis work is partially funded by the E.U. under the contract HPRN-CT-1999-00015. References1. Benfenati, E., Pelagatti, S., Grasso, P., Gini, G.: COMET: the approach of a project in evaluatingtoxicity. In: Gini, G. C.; Katritzky, A. R. (eds.): Predictive Toxicology of Chemicals: Experiences and Impact of AI Tools. AAAI 1999 Spring Symposium Series. AAAI Press, Menlo Park, CA (1999) 40-43 2. Benfenati, E., Piclin, N., Roncaglioni,A., Varì, M.R.: Factors Influencing Predictive Models ForToxicology. SAR and QSAR in environmental research, 12 (2001) 593-603.3. Bishop, C.M.: Neural networks for pattern recognition. Clarendon Press, Oxford (1995)4. 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Minimizing manufacturing costs for thin injectionmolded plastic componentsAbstract：Minimizing the cost of manufacturing a plastic component is very important in the highly competitive plastic injection molding industry.The current approach of R&D work focuses on optimizing the dimensions of the plastic component particularly in reducing the thickness of the component during Product design the first phase of manufacturing in order to minimize the manufacturing cost.。

This approach treats the component dimensions established in the product design phase as the given input, and uses optimization techniques to reduce the manufacturing cost of mold design and molding for producing the component.In most cases, the current approach provides the correct solution for minimizing the manufacturing cost.However, when the approach is applied to a thin component typically when miniaturizing products,it has problems finding the true minimum manufacturing cost. This paper analyses the shortcomings of the current approach for handling thin plastic components and proposes a method to overcome them.A worked example is used to illustrate the problems and compare the differences when using the current approach and the new method proposed in the paper. Keywords Miniaturization of plastic parts Minimization of manufacturing Plastic part design and manufacturing cost .NomenclatureThe thickness of gateThe thickness of the rectangular channelLatent heat offusion ofPP=130kJ/kgThe length of gate=0.5–1.3The length of circular channelThe length of rectangular channelthe consistency index1/Poisson ratio of PP=0.35Plasticmaterial constant,The volume flow rateThe volume flow rateinside the rectangular channelThe volume flow rateinside the circularchannelThe radius of the circularchannelDistance of piston movementLoading time=31536000sTime for making single cavity mold insert=15hDry cycle time=16.5sEjection time=0.009sInjection time=0.5sDemolding temperature of PP=70 CMelt temperature ofPP=190 CThe width of gateThe width of the rectangular channelthe viscosityStrain of materialsStress of materialsThermal conductivity of steel=45W/mKShear stress of plastic materialShear rate of plastic materialPressure drop of spruePressure drop of secondary runnerPressure drop of tertiary runnerPressure drop of gatePressure drop of cavityPressure drop of circular channelPressure drop of rectangular channelJ.K.L.Ho () · K.F.Chu · C.K.MokDepartment of Manufacturing Engineering & Engineering Management,City University of Hong Kong,P.R. China香港大学工程制造与管理学院E-mail: mejohnho@.hkTel.: +852-********Fax: +852-********1 IntroductionIn most industrial applications, the manufacturing cost of a plastic part is mainly governed by the amount of material used in the molding process.Thus, current approaches for plastic part design and manufacturing focus primarily on establishing the minimum part thickness to reduce material usage.The assumption is that designing the mold and molding processes to the minimum thickness requirement should lead to the minimum manufacturing cost. Nowadays, electronic products such as mobile phones and medical devices are becoming ever more complex and their sizes are continually being reduced.The demand for small and thin plastic components for miniaturization assembly has considerably increased in recent years.Other factors besides minimal material usage may also become important when manufacturing thin plastic components.In particular, for thin parts, the injection molding pressure may become significant and has to be considered in the first phase of manufacturing.Employing current design approaches for plastic parts will fail to produce the true minimum manufacturing cost in these cases.Thus, tackling thin plastic parts requires a new approach, alongside existing molddesign principles and molding techniques.1.1Current researchToday, computer-aided simulation software is essential for the design of plastic parts and molds. Such software increases the efficiency of the design process by reducing the design cost and lead time [1].Major systems, such as Mold Flow and C-Flow, use finite element analysis to simulate the filling phenomena, including flow patterns and filling sequences. Thus, the molding conditions can be predicted and validated, so that early design modifications can be achieved. Although available software is capable of analyzing the flow conditions, and the stress and the temperature distribution conditions of the component under various molding scenarios, they do not yield design parameters with minimum manufacturing cost [2,3].The output data of the software only give parameter value ranges for reference and leaves the decision making to the component designer. Several attempts have also been made to optimize the parameters in feeding [4–7], cooling [2,8,9], and ejection These attempts were based on maximizing the flow ability of molten material during the molding process by using empirical relation ships between the product and mold design parameters.Some researchers have made efforts to improve plastic part quality by Reducing the sink mark [11] and the part deformation after molding [12], analyzing the effects of wall thickness and the flow length of the part [13], and analyzing the internal structure of the plastic part design and filling materials flows of the mold design [14]. Reifschneider [15] has compared three types of mold filling simulation programs, including Part Adviser, Fusion, and Insight, with actual experimental testing. All these approaches have established methods that can save a lot of time and cost. However, they just tackled the design parameters of the plastic part and mold individually during the design stage. In addition, they did not provide the design parameters with minimum manufacturing cost.Studies applying various artificial intelligence methods and techniques have been found that mainly focus on optimization analysis of injection molding parameters [16,17]. For in-stance He et al. [3] introduced a fuzzy- neuro approach for automatic resetting of molding process parameters. By contrast , Helps et al. [18,19] adopted artificial neural networks to predict the setting of molding conditions and plastic part quality control in molding. Clearly, the development of comprehensive molding process models and computer-aided manufacturing provides a basis for realizing molding parameter optimization [3 , 16,17]. Mok et al. [20] propose a hybrid neural network and genetic algorithm approach incorporating Case-Based Reasoning (CBR) to derive initial settings for molding parameters for parts with similar design features quickly and with acceptable accuracy. Mok’s approach was based on past product processing data, and was limited to designs that are similar to previous product data. However, no real R&D effort has been found that considers minimizing manufacturing costs for thin plastic components.Generally, the current practical approach for minimizing the manufacturing cost ofplastic components is to minimize the thickness and the dimensions of the part at the product design stage, and then to calculate the costs of the mold design and molding process for the part accordingly, as shown in Fig. 1.The current approach may not be able to obtain the real minimum manufacturing cost when handling thin plastic components.1.2Manufacturing requirements for a typical thin plastic component As a test example, the typical manufacturing requirements for a thin square plastic part with a center hole, as shown in Fig. 2,are given in Table 1.Fig.1. The current practical approachFig.2. Test example of a smallplastic componentTable1. Customer requirements for the example component2 The current practical approachAs shown in Fig.1, the current approach consists of three phases: product design, mold design and molding process parameter setting. A main objective in the product design is to establish the physical dimensions of the part such as its thickness, width and length. The phases of molded sign and molding subsequently treat the established physical dimensions as given inputs to calculate the required details for mold making and molding operations.When applying the current practical approach for tackling the given example, the key variables are handled by the three phases as follows:Product design* Establish the minimum thickness (height) HP, and then calculate the material cost. HP is then treated as a predetermined input for the calculation of the costs of mold design and molding operations. HPMold design* Calculate the cooling time for the determined minimumthickness HP in order to obtain the number of mold cavities required. The mold making cost is then the sum of the costs to machine the:–Depth of cutting (thickness) HP–Number of cavities–Runner diameter DR–Gate thickness HGMolding process* Determine the injection pressure Pin, and then the cost of power consumptionDetermine the cooling time t co, and then the cost of machine operations. The overall molding cost is the sum of the power consumption cost and machine operating cost.The total manufacturing cost is the sum of the costs of plastic material, mold making and molding operations. Note that, in accordance with typical industry practice, all of the following calculations are in terms of unit costs.2.1Product designThis is the first manufacturing phase of the current practical approach. The design minimizes the thickness HP of the plastic component to meet the creep loading deflection constraint , Y (<1.47mmafter1yearofusage),and to minimize plastic material usage cost Cm. Minimizing HP requires [21]:Figure 3 plots changes in HP through Eqs.1 and 2.The graphs show that the smallest thickness that meets the 1.47mm maximum creep deflection constraint is 0 .75mm,with a plastic material cost of $0.000483558/unit and a batch size of 200000 units.This thickness will be treated as a given input for the subsequent molded sign and molding process analysis phases.2.2Mold design2.2.1 Determination of cooling timeThe desired mold temperature is 25 C. The determined thickness is 0.75mm. Figure 4 shows the cooling channels layout following standard industry practices. The cooling channel diameter is chosen to be 3mm for this example.From [22], the cooling time t co:And the location factor,BysolvingEqs.3and4, and substituting HP =0.75mm and the given values of the cooling channel design parameters, the cooling time (3.1s) is obtained.The cycle time t cycle, given by E q. 5, is proportional to the molding machine operating costs, and consists of injection time (t in), ejection time (t e j), dry cycle time (t d c), and cooling time (t c o).2.2.2 Determination of the number of mold cavities In general, the cost of mold making depends on the amount of machining work to form the required number of cores/cavities, runners, and gates. The given example calls for a two-plate moldFig.3.Deflection and plastic materials costs versus part thickness Fig.4. Cooling channel layout that does not require undercut machining. Therefore, the ma chining work for cutting the runners and gates is proportional to the work involved in forming the cores/cavities and need not be considered. In the example, mold making cost Cmm is governed by (n, HP).Generally, the minimum number of cavities, Nmin, is chosen to allow for delivery of the batch of plastic parts on time图3 。

2021年第4期（总第285期） 畜牧生产13提高奶牛性控冻精配种受胎率的技术与管理措施柳明训（山东省莱西市河头店人民政府，山东 莱西 266621）中图分类号：S823.9+1 文献标识码：B 文章编号：1007-1733（2021）04-0013-02 近年来，奶牛性控冻精在奶牛生产中已得到了广泛的应用，用性控冻精配种，可使母牛的产犊效益显著提高。

由于性控冻精成本比普通冻精高出十多倍，而且每剂精液中有效精子数量也比普通冻精要少得多，能取得较高受胎率的难度较大，这就使奶牛性控冻精的应用受到了很大的限制。

因此，为了应用奶牛性控冻精能够取得较为理想的使用效果，根据笔者多年工作经验，总结出如下技术要求。

1 性控冻精应用技术1.1 精液品质检查 解冻所需盛温水的器具最好采用容量较大的容器，如用铝饭盒、广口保温瓶等。

解冻前先将镊子尖端接触液氮预冷，再将盛放细管冻精的提筒（内盛细管冻精纱布袋），提到距离颈管上口以下约8 cm 处，然后迅速镊住一支细管冻精放入盛有40 ℃ 温水的器具内，用镊子夹住细管轻轻摇动30~40 s ，使管内冻精迅速融化。

将细管从温水中取出，用灭菌纸巾擦干，立即用剪子将细管密封一端剪齐，挤出一小滴精液于载波片上，盖上盖玻片，用放大400倍的显微镜进行镜检。

凡用于输精的细管精液，精子活力不应低于30 %，有效精子数应在200万个以上。

1.2 奶牛选择 首先是奶牛的选择，应选择中、高产奶牛及其后代作为使用对象。

其次是年龄和胎次，首选初配母牛和生产3胎以内的母牛。

再次是营养和健康状况，要求膘情适中，健康无疾病和繁殖疾病史。

1.3 搞好发情鉴定，做到适时输精 奶牛适时输精的时间主要是根据母牛卵巢上的卵泡发育成熟情况与外部发情表现相结合，进行综合判断。

一般是在发情末期到发情结束后3~4 h 为宜。

外部表现：阴户肿胀减退，生殖道排出黏液量少而黏稠。

输精时要做到输精部位准确，一般输到子宫体。

每个情期输精1~2次，1支/次细管冻精，两次输精的间隔时间为8 h 左右，输精时要掌握慢参考文献[1] 张震, 闫磊, 闫跃飞, 等. DHI 助推奶牛养殖水平大幅提高[J]. 中国畜牧业, 2016（23）: 27-29.[2] 河北省人民政府关于加快推进奶业振兴的实施意见[J].北方牧业, 2019（13）: 4-5.[3] 郑国生, 施正香, 滕光辉. 中国奶牛养殖设施装备技术研究进展[J]. 中国畜牧杂志, 2019, 55（7）: 169-174. [4] P. Zappavigna, P. Liberati, U. Chiappini. Feeding ControlSystem for Dairy Cows[J]. Journal of Agricultural Engineering Research, 1998, 71（4）.[5] Gupta G S, Barlow P, Chapman R. Development ofanautomated cattle feed mixer: sixth ieee international symposiumon electronic design, test and application[C]. Queenstown: Ieee, 2011.[6] 翟改霞, 贺刚, 戴晓军, 等. 智能化犊牛饲喂系统及国外典型机型[J]. 农业工程, 2015, 5（4）: 5-8.[7] Pastell M, Takko H, Grohn H, et al. Assessingcows’welfare: weighing the cow in a milking robot[J]. Biosyst Eng, 2006, 93（1）: 81-87.[8] Hogeveen H, Ouweltjes W, Koning C J A.M, et al .Milkinginterval, milk production and milk flow-rate in an automaticmilking system[J]. Livest Prod Sci, 2001, 72（1-2）: 157-167.[9] Pan L, Yang S X. Analysing livestock farm odour usinganadaptive neuro-fuzzy approach[J]. Biosyst Eng, 2007, 97（3）: 387-393.[10] 乔希. 山东省奶牛养殖场（户）清洁生产行为实证研究[D]. 泰安: 山东农业大学, 2019.（收稿日期：2021–01–06）山东畜牧兽医 2021年第42卷14 插、适深、轻注、缓出，防止精液倒流。

CCh ak ra bo rt y, www.my re ad er s.i nf oRFuzzy Set Theory : Soft Computing Course Lecture 29 – 34, notes, slides/ , RC Chakraborty, e-mail rcchak@ , Aug . 10, 2010/html/soft_computing.htmlFuzzy Set TheorySoft ComputingReturn to WebsiteIntroduction to fuzzy set, topics : classical set theory, fuzzy set theory, crisp and non-crisp Sets representation, capturing uncertainty, examples. Fuzzy membership and graphic interpretationof fuzzy sets - small, prime numbers, universal, finite, infinite, empty space; Fuzzy Operations -inclusion, comparability, equality, complement, union, intersection, difference; Fuzzy properties related to union, intersection, distributivity, law of excluded middle, law of contradiction, and cartesian product. Fuzzy relations : definition, examples, forming fuzzy relations, projections of fuzzy relations, max-min and min-max compositions.CCh ak ra bo rt y, www.my re ad er s.i nf oRFuzzy Set TheorySoft ComputingTopics(Lectures 29, 30, 31, 32, 33, 34 6 hours)Slides 1. Introduction to fuzzy SetWhat is Fuzzy set? Classical set theory; Fuzzy set theory; Crisp and Non-crisp Sets : Representation; Capturing uncertainty, Examples03-102. Fuzzy setFuzzy Membership; Graphic interpretation of fuzzy sets : small, prime numbers, universal, finite, infinite, empty space;Fuzzy Operations : Inclusion, Comparability, Equality, Complement, Union, Intersection, Difference;Fuzzy Properties : Related to union – Identity, Idempotence, Associativity, Commutativity ; Related to Intersection – Absorption, Identity, Idempotence, Commutativity, Associativity; Additional properties - Distributivity, Law of excluded middle, Law of contradiction; Cartesian product .11-323. Fuzzy RelationsDefinition of Fuzzy Relation, examples;Forming Fuzzy Relations – Membership matrix, Graphical form; Projections of Fuzzy Relations – first, second and global; Max-Min and Min-Max compositions.33-414. References4202C Ch ak ra bo rt y, www.my re ad er s.i nf oRFuzzy Set TheoryWhat is Fuzzy Set ?• The word "fuzzy" means "vagueness ". Fuzziness occurs when theboundary of a piece of information is not clear-cut.• Fuzzy sets have been introduced by Lotfi A. Zadeh (1965) as anextension of the classical notion of set.• Classical set theory allows the membership of the elements in the setin binary terms, a bivalent condition - an element either belongs or does not belong to the set.Fuzzy set theory permits the gradual assessment of the membership of elements in a set, described with the aid of a membership function valued in the real unit interval [0, 1].• Example:Words like young, tall, good , or high are fuzzy.− There is no single quantitative value which defines the term young. − For some people, age 25 is young, and for others, age 35 is young. − The concept young has no clean boundary.− Age 1 is definitely young and age 100 is definitely not young; − Age 35 has some possibility of being young and usually dependson the context in which it is being considered.03CCh ak ra bo rt y, www.my re ad er s.i nf oRSC - Fuzzy set theory - Introduction1. IntroductionIn real world, there exists much fuzzy knowledge;Knowledge that is vague, imprecise, uncertain, ambiguous, inexact , or probabilistic in nature.Human thinking and reasoning frequently involve fuzzy information, originating from inherently inexact human concepts. Humans, can give satisfactory answers, which are probably true.However, our systems are unable to answer many questions. The reason is, most systems are designed based upon classical set theory and two-valued logic which is unable to cope with unreliable and incomplete information and give expert opinions.We want, our systems should also be able to cope with unreliable and incomplete information and give expert opinions. Fuzzy sets have been able provide solutions to many real world problems.Fuzzy Set theory is an extension of classical set theory where elements have degrees of membership.04CCh ak ra bo rt y, www.my re R• Classical Set TheoryA Set is any well defined collection of objects. An object in a set is called an element or member of that set.− Sets are defined by a simple statement describing whether aparticular element having a certain property belongs to that particular set.− Classical set theory enumerates all its elements usingA = { a 1 , a 2 , a 3 , a 4 , . . . . a n }If the elements a i (i = 1, 2, 3, . . . n ) of a set A are subset ofuniversal set X , then set A can be represented for all elementsx ∈ X by its characteristic function1 if x ∈ XµA (x) = 0 otherwise− A set A is well described by a function called characteristicfunction .This function, defined on the universal space X , assumes :a value of 1 for those elements x that belong to set A , and a value of 0 for those elements x that do not belong to set A .The notations used to express these mathematically areΑ : Χ → [0, 1]A(x) = 1 , x is a member of A Eq.(1) A(x) = 0 , x is not a member of AAlternatively, the set A can be represented for all elements x ∈ X by its characteristic function µA (x) defined as1 if x ∈ XµA (x) = Eq.(2) 0 otherwise− Thus in classical set theory µA (x) has only the values 0('false')and 1 ('true''). Such sets are called crisp sets.05CCh ak ra bo rt y, www.my re R• Fuzzy Set TheoryFuzzy set theory is an extension of classical set theory where elements have varying degrees of membership. A logic based on the two truth values, True and False , is sometimes inadequate when describing human reasoning. Fuzzy logic uses the whole interval between0 (false) and 1 (true) to describe human reasoning.− A Fuzzy Set is any set that allows its members to have differentdegree of membership, called membership function , in the interval[0 , 1].− The degree of membership or truth is not same as probability;fuzzy truth is not likelihood of some event or condition. fuzzy truth represents membership in vaguely defined sets;− Fuzzy logic is derived from fuzzy set theory dealing with reasoningthat is approximate rather than precisely deduced from classical predicate logic.− Fuzzy logic is capable of handling inherently imprecise concepts.− Fuzzy logic allows in linguistic form the set membership values toimprecise concepts like "slightly", "quite" and "very".− Fuzzy set theory defines Fuzzy Operators on Fuzzy Sets.06CCh ak ra bo rt y, www.my re R• Crisp and Non-Crisp Set− As said before, in classical set theory, the characteristic functionµA (x) of Eq.(2) has only values 0 ('false') and 1 ('true''). Such sets are crisp sets.− For Non-crisp sets the characteristic function µA (x) can be defined.The characteristic function µA (x) of Eq. (2) for the crisp set isgeneralized for the Non-crisp sets.This generalized characteristic function µA (x) of Eq.(2) is called membership function .Such Non-crisp sets are called Fuzzy Sets .− Crisp set theory is not capable of representing descriptions andclassifications in many cases; In fact, Crisp set does not provide adequate representation for most cases.− The proposition of Fuzzy Sets are motivated by the need to captureand represent real world data with uncertainty due to imprecise measurement.− The uncertainties are also caused by vagueness in the language.07CCh ak ra bo rt y, www.my re R• Representation of Crisp and Non-Crisp SetExample : Classify students for a basketball team This example explains the grade of truth value.- tall students qualify and not tall students do not qualify - if students 1.8 m tall are to be qualified, then should we exclude a student who is 1/10" less? orshould we exclude a student who is 1" shorter?■ Non-Crisp Representation to represent the notion of a tall person.Crisp logic Non-crisp logicFig. 1 Set Representation – Degree or grade of truthA student of height 1.79m would belong to both tall and not tall sets with a particular degree of membership.As the height increases the membership grade within the tall set would increase whilst the membership grade within the not-tall set would decrease.08CCh ak ra bo rt y, www.my re R• Capturing UncertaintyInstead of avoiding or ignoring uncertainty, Lotfi Zadeh introduced Fuzzy Set theory that captures uncertainty.■ A fuzzy set is described by a membership function µA (x) of A .This membership function associates to each element x σ ∈ X a number as µA (x σ ) in the closed unit interval [0, 1].The number µA (x σ ) represents the degree of membership of x σ in A .■ The notation used for membership function µA(x) of a fuzzy set A isΑ : Χ → [0, 1]■ Each membership function maps elements of a given universal baseset X , which is itself a crisp set, into real numbers in [0, 1] .■ ExampleFig. 2 Membership function of a Crisp set C and Fuzzy set F■ In the case of Crisp Sets the members of a set are :either out of the set, with membership of degree " 0 ", or in the set, with membership of degree " 1 ",Therefore, Crisp Sets ⊆ Fuzzy SetsIn other words, Crisp Sets are Special cases of Fuzzy Sets.[Continued in next slide]09CCh ak ra bo rt y, www.my re R• Examples of Crisp and Non-Crisp SetExample 1: Set of prime numbers ( a crisp set )If we consider space X consisting of natural numbers ≤ 12 ie X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}Then, the set of prime numbers could be described as follows.PRIME = {x contained in X | x is a prime number} = {2, 3, 5, 6, 7, 11}Example 2: Set of SMALL ( as non-crisp set )A Set X that consists of SMALL cannot be described ;for example 1 is a member of SMALL and 12 is not a member of SMALL .Set A , as SMALL, has un-sharp boundaries, can be characterized by a function that assigns a real number from the closed interval from 0 to 1to each element x in the set X .10CCh ak ra bo rt y, ww w .my re ad er s.i nf oRSC - Fuzzy set theory – Fuzzy Set2. Fuzzy SetA Fuzzy Set is any set that allows its members to have different degreeof membership, called membership function, in the interval [0 , 1].• Definition of Fuzzy setA fuzzy set A , defined in the universal space X , is a function defined in X which assumes values in the range [0, 1].A fuzzy set A is written as a set of pairs {x, A(x)} asA = {{x , A(x)}} , x in the set Xwhere x is an element of the universal space X , andA(x) is the value of the function A for this element.The value A(x) is the membership grade of the element x in a fuzzy set A .Example : Set SMALL in set X consisting of natural numbers ≤ to 12.Assume: SMALL(1) = 1, SMALL(2) = 1, SMALL(3) = 0.9, SMALL(4) = 0.6,SMALL(5) = 0.4, SMALL(6) = 0.3, SMALL(7) = 0.2, SMALL(8) = 0.1, SMALL(u) = 0 for u >= 9.Then, following the notations described in the definition above :Set SMALL = {{1, 1 }, {2, 1 }, {3, 0.9}, {4, 0.6}, {5, 0.4}, {6, 0.3}, {7, 0.2},{8, 0.1}, {9, 0 }, {10, 0 }, {11, 0}, {12, 0}}Note that a fuzzy set can be defined precisely by associating with each x , its grade of membership in SMALL .11CCh ak ra bo rt y, www.my re R• Definition of Universal SpaceOriginally the universal space for fuzzy sets in fuzzy logic was defined only on the integers. Now, the universal space for fuzzy sets and fuzzy relations is defined with three numbers.The first two numbers specify the start and end of the universal space, and the third argument specifies the increment between elements. This gives the user more flexibility in choosing the universal space.Example : The fuzzy set of numbers, defined in the universal spaceX = { x i } = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} is presented as SetOption [FuzzySet, UniversalSpace → {1, 12, 1}]12CCh ak ra bo rt y, www.my re R2.1 Fuzzy MembershipA fuzzy set A defined in the universal space X is a function defined in X which assumes values in the range [0, 1].A fuzzy set A is written as a set of pairs {x, A(x)}.A = {{x , A(x)}} , x in the set Xwhere x is an element of the universal space X , and A(x) is the value of the function A for this element.The value A(x) is the degree of membership of the element x in a fuzzy set A .The Graphic Interpretation of fuzzy membership for the fuzzy sets : Small, Prime Numbers, Universal-space, Finite and Infinite UniversalSpace, and Empty are illustrated in the next few slides.13CCh ak ra bo rt y, www.my re R• Graphic Interpretation of Fuzzy Sets SMALLThe fuzzy set SMALL of small numbers, defined in the universal spaceX = { x i } = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} is presented as SetOption [FuzzySet, UniversalSpace → {1, 12, 1}]The Set SMALL in set X is :SMALL = FuzzySet {{1, 1 }, {2, 1 }, {3, 0.9}, {4, 0.6}, {5, 0.4}, {6, 0.3},{7, 0.2}, {8, 0.1}, {9, 0 }, {10, 0 }, {11, 0}, {12, 0}}Therefore SetSmall is represented asSetSmall = FuzzySet [{{1,1},{2,1}, {3,0.9}, {4,0.6}, {5,0.4},{6,0.3}, {7,0.2},{8, 0.1}, {9, 0}, {10, 0}, {11, 0}, {12, 0}} , UniversalSpace → {1, 12, 1}]FuzzyPlot [ SMALL, AxesLable → {"X", "SMALL"}]SMALLFig Graphic Interpretation of Fuzzy Sets SMALL140 .8 .2 .4 .61CCh ak ra bo rt y, www.my re R• Graphic Interpretation of Fuzzy Sets PRIME NumbersThe fuzzy set PRIME numbers, defined in the universal spaceX = { x i } = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} is presented as SetOption [FuzzySet, UniversalSpace → {1, 12, 1}]The Set PRIME in set X is :PRIME = FuzzySet {{1, 0}, {2, 1}, {3, 1}, {4, 0}, {5, 1}, {6, 0}, {7, 1}, {8, 0},{9, 0}, {10, 0}, {11, 1}, {12, 0}}Therefore SetPrime is represented asSetPrime = FuzzySet [{{1,0},{2,1}, {3,1}, {4,0}, {5,1},{6,0}, {7,1},{8, 0}, {9, 0}, {10, 0}, {11, 1}, {12, 0}} , UniversalSpace → {1, 12, 1}]FuzzyPlot [ PRIME, AxesLable → {"X", "PRIME"}]PRIMEFig Graphic Interpretation of Fuzzy Sets PRIME15.8 .2 .4 .6 1CCh ak ra bo rt y, www.my re R• Graphic Interpretation of Fuzzy Sets UNIVERSALSPACEIn any application of sets or fuzzy sets theory, all sets are subsets of a fixed set called universal space or universe of discourse denoted by X . Universal space X as a fuzzy set is a function equal to 1 for all elements.The fuzzy set UNIVERSALSPACE numbers, defined in the universal space X = { x i } = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} is presented asSetOption [FuzzySet, UniversalSpace → {1, 12, 1}]The Set UNIVERSALSPACE in set X is :UNIVERSALSPACE = FuzzySet {{1, 1}, {2, 1}, {3, 1}, {4, 1}, {5, 1}, {6, 1},{7, 1}, {8, 1}, {9, 1}, {10, 1}, {11, 1}, {12, 1}}Therefore SetUniversal is represented asSetUniversal = FuzzySet [{{1,1},{2,1}, {3,1}, {4,1}, {5,1},{6,1}, {7,1},{8, 1}, {9, 1}, {10, 1}, {11, 1}, {12, 1}} , UniversalSpace → {1, 12, 1}]FuzzyPlot [ UNIVERSALSPACE , AxesLable → {"X", " UNIVERSAL SPACE "}]UNIVERSAL SPACEFig Graphic Interpretation of Fuzzy Set UNIVERSALSPACE16.8 .2 .4 .6 1CCh ak ra bo rt y, www.my re R• Finite and Infinite Universal SpaceUniversal sets can be finite or infinite.Any universal set is finite if it consists of a specific number of different elements, that is, if in counting the different elements of the set, the counting can come to an end, else the set is infinite.Examples:1. Let N be the universal space of the days of the week. N = {Mo, Tu, We, Th, Fr, Sa, Su}. N is finite.2. Let M = {1, 3, 5, 7, 9, ...}. M is infinite.3. Let L = {u | u is a lake in a city }. L is finite. (Although it may be difficult to count the number of lakes in a city,but L is still a finite universal set.)17CCh ak ra bo rt y, www.my re R• Graphic Interpretation of Fuzzy Sets EMPTYAn empty set is a set that contains only elements with a grade of membership equal to 0.Example: Let EMPTY be a set of people, in Minnesota, older than 120. The Empty set is also called the Null set .The fuzzy set EMPTY , defined in the universal space X = { x i } = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} is presented asSetOption [FuzzySet, UniversalSpace → {1, 12, 1}]The Set EMPTY in set X is :EMPTY = FuzzySet {{1, 0}, {2, 0}, {3, 0}, {4, 0}, {5, 0}, {6, 0}, {7, 0},{8, 0}, {9, 0}, {10, 0}, {11, 0}, {12, 0}}Therefore SetEmpty is represented asSetEmpty = FuzzySet [{{1,0},{2,0}, {3,0}, {4,0}, {5,0},{6,0}, {7,0},{8, 0}, {9, 0}, {10, 0}, {11, 0}, {12, 0}} , U niversalSpace → {1, 12, 1}]FuzzyPlot [ EMPTY, AxesLable → {"X", " UNIVERSAL SPACE "}]EMPTYFig Graphic Interpretation of Fuzzy Set EMPTY18.8 .2 .4 .6 1CCh ak ra bo rt y, www.my re R2.2 Fuzzy OperationsA fuzzy set operations are the operations on fuzzy sets. The fuzzy setoperations are generalization of crisp set operations. Zadeh [1965] formulated the fuzzy set theory in the terms of standard operations: Complement, Union, Intersection, and Difference.In this section, the graphical interpretation of the following standard fuzzy set terms and the Fuzzy Logic operations are illustrated:Inclusion : FuzzyInclude [VERYSMALL, SMALL] Equality : FuzzyEQUALITY [SMALL, STILLSMALL] Complement : FuzzyNOTSMALL = FuzzyCompliment [Small] Union : FuzzyUNION = [SMALL ∪ MEDIUM]Intersection :FUZZYINTERSECTON = [SMALL ∩ MEDIUM]19CCh ak ra bo rt y, www.my re R• InclusionLet A and B be fuzzy sets defined in the same universal space X . The fuzzy set A is included in the fuzzy set B if and only if for every x in the set X we have A(x) ≤ B(x)Example :The fuzzy set UNIVERSALSPACE numbers, defined in the universal space X = { x i } = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} is presented asSetOption [FuzzySet, UniversalSpace → {1, 12, 1}]The fuzzy set B SMALLThe Set SMALL in set X is :SMALL = FuzzySet {{1, 1 }, {2, 1 }, {3, 0.9}, {4, 0.6}, {5, 0.4}, {6, 0.3},{7, 0.2}, {8, 0.1}, {9, 0 }, {10, 0 }, {11, 0}, {12, 0}}Therefore SetSmall is represented asSetSmall = FuzzySet [{{1,1},{2,1}, {3,0.9}, {4,0.6}, {5,0.4},{6,0.3}, {7,0.2},{8, 0.1}, {9, 0}, {10, 0}, {11, 0}, {12, 0}} , UniversalSpace → {1, 12, 1}]The fuzzy set A VERYSMALLThe Set VERYSMALL in set X is :VERYSMALL = FuzzySet {{1, 1 }, {2, 0.8 }, {3, 0.7}, {4, 0.4}, {5, 0.2},{6, 0.1}, {7, 0 }, {8, 0 }, {9, 0 }, {10, 0 }, {11, 0}, {12, 0}}Therefore SetVerySmall is represented asSetVerySmall = FuzzySet [{{1,1},{2,0.8}, {3,0.7}, {4,0.4}, {5,0.2},{6,0.1},{7,0}, {8, 0}, {9, 0}, {10, 0}, {11, 0}, {12, 0}} , UniversalSpace → {1, 12, 1}]The Fuzzy Operation : Inclusion Include [VERYSMALL, SMALL]Fig Graphic Interpretation of Fuzzy InclusionFuzzyPlot [SMALL, VERYSMALL ]201 .2.6.4.8CCh ak ra bo rt y, www.my re R• ComparabilityTwo fuzzy sets A and B are comparable if the condition A ⊂ B or B ⊂ A holds, ie,if one of the fuzzy sets is a subset of the other set, they are comparable.Two fuzzy sets A and B are incomparable If the condition A ⊄ B or B ⊄ A holds.Example 1:Let A = {{a, 1}, {b, 1}, {c, 0}} andB = {{a, 1}, {b, 1}, {c, 1}}.Then A is comparable to B , since A is a subset of B .Example 2 :Let C = {{a, 1}, {b, 1}, {c, 0.5}} andD = {{a, 1}, {b, 0.9}, {c, 0.6}}.Then C and D are not comparable sinceC is not a subset ofD and D is not a subset of C .Property Related to Inclusion :for all x in the set X , if A(x) ⊂ B(x) ⊂ C(x), then accordingly A ⊂ C.21CCh ak ra bo rt y, www.my re R• EqualityLet A and B be fuzzy sets defined in the same space X . Then A and B are equal, which is denoted X = Y if and only if for all x in the set X , A(x) = B(x).Example.The fuzzy set B SMALLSMALL = FuzzySet {{1, 1 }, {2, 1 }, {3, 0.9}, {4, 0.6}, {5, 0.4}, {6, 0.3},{7, 0.2}, {8, 0.1}, {9, 0 }, {10, 0 }, {11, 0}, {12, 0}}The fuzzy set A STILLSMALLSTILLSMALL = FuzzySet {{1, 1 }, {2, 1 }, {3, 0.9}, {4, 0.6}, {5, 0.4},{6, 0.3}, {7, 0.2}, {8, 0.1}, {9, 0 }, {10, 0 }, {11, 0}, {12, 0}}The Fuzzy Operation : Equality Equality [SMALL, STILLSMALL]Fig Graphic Interpretation of Fuzzy EqualityFuzzyPlot [SMALL, STILLSMALL]Note : If equality A(x) = B(x) is not satisfied even for one element x in the set X , then we say that A is not equal to B .221 .2.6 .4 .8CCh ak ra bo rt y, www.my re R• ComplementLet A be a fuzzy set defined in the space X .Then the fuzzy set B is a complement of the fuzzy set A , if and only if, for all x in the set X , B(x) = 1 - A(x).The complement of the fuzzy set A is often denoted by A' or A cFuzzy Complement : Ac(x) = 1 – A(x) Example 1.The fuzzy set A SMALLSMALL = FuzzySet {{1, 1 }, {2, 1 }, {3, 0.9}, {4, 0.6}, {5, 0.4}, {6, 0.3},{7, 0.2}, {8, 0.1}, {9, 0 }, {10, 0 }, {11, 0}, {12, 0}}The fuzzy set Ac NOTSMALLNOTSMALL = FuzzySet {{1, 0 }, {2, 0 }, {3, 0.1}, {4, 0.4}, {5, 0.6}, {6, 0.7},{7, 0.8}, {8, 0.9}, {9, 1 }, {10, 1 }, {11, 1}, {12, 1}}The Fuzzy Operation : ComplimentNOTSMALL = Compliment [SMALL]Fig Graphic Interpretation of Fuzzy ComplimentFuzzyPlot [SMALL, NOTSMALL]230 1 .2 .6.4.8CCh ak ra bo rt y, www.my re RExample 2.The empty set Φ and the universal set X , as fuzzy sets, are complements of one another.Φ' = X , X' = ΦThe fuzzy set B EMPTYEmpty = FuzzySet {{1, 0 }, {2, 0 }, {3, 0}, {4, 0}, {5, 0}, {6, 0},{7, 0}, {8, 0}, {9, 0 }, {10, 0 }, {11, 0}, {12, 0}}The fuzzy set A UNIVERSALUniversal = FuzzySet {{1, 1 }, {2, 1 }, {3, 1}, {4, 1}, {5, 1}, {6, 1},{7, 1}, {8, 1}, {9, 1 }, {10, 1 }, {11, 1}, {12, 1}}The fuzzy operation : ComplimentEMPTY = Compliment [UNIVERSALSPACE ] Membership Grade B AFig Graphic Interpretation of Fuzzy ComplimentFuzzyPlot [EMPTY, UNIVERSALSPACE]241 .2.6 .4 .8CCh ak ra bo rt y, www.my re R• UnionLet A and B be fuzzy sets defined in the space X .The union is defined as the smallest fuzzy set that contains both A and B . The union of A and B is denoted by A ∪ B.The following relation must be satisfied for the union operation :for all x in the set X, (A ∪ B)(x) = Max (A(x), B(x)).Fuzzy Union : (A ∪ B)(x) = max [A(x), B(x)] for all x ∈ X Example 1 : Union of Fuzzy A and BA(x) = 0.6 and B(x) = 0.4 ∴ (A ∪ B)(x) = max [0.6, 0.4] = 0.6Example 2 : Union of SMALL and MEDIUMThe fuzzy set A SMALLSMALL = FuzzySet {{1, 1 }, {2, 1 }, {3, 0.9}, {4, 0.6}, {5, 0.4}, {6, 0.3},{7, 0.2}, {8, 0.1}, {9, 0 }, {10, 0 }, {11, 0}, {12, 0}}The fuzzy set B MEDIUMMEDIUM = FuzzySet {{1, 0 }, {2, 0 }, {3, 0}, {4, 0.2}, {5, 0.5}, {6, 0.8},{7, 1}, {8, 1}, {9, 0.7 }, {10, 0.4 }, {11, 0.1}, {12, 0}}The fuzzy operation : UnionFUZZYUNION = [SMALL ∪ MEDIUM]SetSmallUNIONMedium = FuzzySet [{{1,1},{2,1}, {3,0.9}, {4,0.6}, {5,0.5}, {6,0.8}, {7,1}, {8, 1}, {9, 0.7}, {10, 0.4}, {11, 0.1}, {12, 0}} , UniversalSpace → {1, 12, 1}]Fig Graphic Interpretation of Fuzzy UnionFuzzyPlot [UNION]The notion of the union is closely related to that of the connective "or ".Let A is a class of "Young" men, B is a class of "Bald" men.If "David is Young" or "David is Bald," then David is associated with the union of A and B . Implies David is a member of A ∪ B .251 .2 .6.4 .8CCh ak ra bo rt y, www.my re R• IntersectionLet A and B be fuzzy sets defined in the space X . Intersection is defined as the greatest fuzzy set that include both A and B . Intersection of A and B is denoted by A ∩ B. The following relation must be satisfied for the intersection operation :for all x in the set X, (A ∩ B)(x) = Min (A(x), B(x)).Fuzzy Intersection : (A ∩ B)(x) = min [A(x), B(x)] for all x ∈ XExample 1 : Intersection of Fuzzy A and BA(x) = 0.6 and B(x) = 0.4 ∴ (A ∩ B)(x) = min [0.6, 0.4] = 0.4Example 2 : Union of SMALL and MEDIUMThe fuzzy set A SMALLSMALL = FuzzySet {{1, 1 }, {2, 1 }, {3, 0.9}, {4, 0.6}, {5, 0.4}, {6, 0.3},{7, 0.2}, {8, 0.1}, {9, 0 }, {10, 0 }, {11, 0}, {12, 0}}The fuzzy set B MEDIUMMEDIUM = FuzzySet {{1, 0 }, {2, 0 }, {3, 0}, {4, 0.2}, {5, 0.5}, {6, 0.8},{7, 1}, {8, 1}, {9, 0.7 }, {10, 0.4 }, {11, 0.1}, {12, 0}}The fuzzy operation : IntersectionFUZZYINTERSECTION = min [SMALL ∩ MEDIUM]SetSmallINTERSECTIONMedium = FuzzySet [{{1,0},{2,0}, {3,0}, {4,0.2},{5,0.4}, {6,0.3}, {7,0.2}, {8, 0.1}, {9, 0}, {10, 0}, {11, 0}, {12, 0}} , UniversalSpace → {1, 12, 1}]Membership Grade FUZZYINTERSECTON = [SMALL ∩ MEDIUM]Fig Graphic Interpretation of Fuzzy UnionFuzzyPlot [INTERSECTION]261 .2.6 .4 .8CCh ak ra bo rt y, www.my re R• DifferenceLet A and B be fuzzy sets defined in the space X . The difference of A and B is denoted by A ∩ B'.Fuzzy Difference : (A - B)(x) = min [A(x), 1- B(x)] for all x ∈ XExample : Difference of MEDIUM and SMALLThe fuzzy set A MEDIUMMEDIUM = FuzzySet {{1, 0 }, {2, 0 }, {3, 0}, {4, 0.2}, {5, 0.5}, {6, 0.8},{7, 1}, {8, 1}, {9, 0.7 }, {10, 0.4 }, {11, 0.1}, {12, 0}}The fuzzy set B SMALLMEDIUM = FuzzySet {{1, 1 }, {2, 1 }, {3, 0.9}, {4, 0.6}, {5, 0.4}, {6, 0.3},{7, 0.2}, {8, 0.1}, {9, 0.7 }, {10, 0.4 }, {11, 0}, {12, 0}}Fuzzy Complement : Bc(x) = 1 – B(x)The fuzzy set Bc NOTSMALLNOTSMALL = FuzzySet {{1, 0 }, {2, 0 }, {3, 0.1}, {4, 0.4}, {5, 0.6}, {6, 0.7},{7, 0.8}, {8, 0.9}, {9, 1 }, {10, 1 }, {11, 1}, {12, 1}}The fuzzy operation : Difference by the definition of DifferenceFUZZYDIFFERENCE = [MEDIUM ∩ SMALL']SetMediumDIFFERECESmall = FuzzySet [{{1,0},{2,0}, {3,0}, {4,0.2},{5,0.5}, {6,0.7}, {7,0.8}, {8, 0.9}, {9, 0.7},{10, 0.4}, {11, 0.1}, {12, 0}} , UniversalSpace → {1, 12, 1}]Membership Grade FUZZYDIFFERENCE = [MEDIUM ∪ SMALL' ]Fig Graphic Interpretation of Fuzzy UnionFuzzyPlot [UNION]271 .2 .6 .4 .8。

HAZOP e Local approach in the Mexican oil &gas industryM.Pérez-Marín a ,M.A.Rodríguez-Toral b ,*aInstituto Mexicano del Petróleo,Dirección de Seguridad y Medio Ambiente,Eje Central Lázaro Cárdenas Norte No.152,07730México,D.F.,Mexicob PEMEX,Dirección Corporativa de Operaciones,Gerencia de Análisis de Inversiones,Torre Ejecutiva,Piso 12,Av.Marina Nacional No.329,11311México,D.F.,Mexicoa r t i c l e i n f oArticle history:Received 3September 2012Received in revised form 26March 2013Accepted 27March 2013Keywords:HAZOPRisk acceptance criteria Oil &gasa b s t r a c tHAZOP (Hazard and Operability)studies began about 40years ago,when the Process Industry and complexity of its operations start to massively grow in different parts of the world.HAZOP has been successfully applied in Process Systems hazard identi fication by operators,design engineers and consulting firms.Nevertheless,after a few decades since its first applications,HAZOP studies are not truly standard in worldwide industrial practice.It is common to find differences in its execution and results format.The aim of this paper is to show that in the Mexican case at National level in the oil and gas industry,there exist an explicit acceptance risk criteria,thus impacting the risk scenarios prioritizing process.Although HAZOP studies in the Mexican oil &gas industry,based on PEMEX corporate standard has precise acceptance criteria,it is not a signi ficant difference in HAZOP applied elsewhere,but has the advantage of being fully transparent in terms of what a local industry is willing to accept as the level of risk acceptance criteria,also helps to gain an understanding of the degree of HAZOP applications in the Mexican oil &gas sector.Contrary to this in HAZOP ISO standard,risk acceptance criteria is not speci fied and it only mentions that HAZOP can consider scenarios ranking.The paper concludes indicating major implications of risk ranking in HAZOP,whether before or after safeguards identi fication.Ó2013Elsevier Ltd.All rights reserved.1.IntroductionHAZOP (Hazard and Operability)studies appeared in systematic way about 40years ago (Lawley,1974)where a multidisciplinary group uses keywords on Process variables to find potential hazards and operability troubles (Mannan,2012,pp.8-31).The basic prin-ciple is to have a full process description and to ask in each node what deviations to the design purpose can occur,what causes produce them,and what consequences can be presented.This is done systematically by applying the guide words:Not ,More than ,Less than ,etc.as to generate a list of potential failures in equipment and process components.The objective of this paper is to show that in the Mexican case at National level in the oil and gas industry,there is an explicit acceptance risk criteria,thus impacting the risk scenarios priori-tizing process.Although HAZOP methodology in the Mexican oil &gas industry,based on PEMEX corporate standard has precise acceptance criteria,it is not a signi ficant difference in HAZOP studies applied elsewhere,but has the advantage of being fullytransparent in terms of what a local industry is willing to accept as the level of risk acceptance criteria,also helps to gain an under-standing of the degree of HAZOP applications in the Mexican oil &gas sector.Contrary to this in HAZOP ISO standard (ISO,2000),risk acceptance criteria is not speci fied and it only mentions that HAZOP can consider scenarios ranking.The paper concludes indicating major implications of risk prioritizing in HAZOP,whether before or after safeguards identi fication.2.Previous workHAZOP studies include from original ICI method with required actions only,to current applications based on computerized documentation,registering design intentions at nodes,guide words,causes,deviations,consequences,safeguards,cause fre-quencies,loss contention impact,risk reduction factors,scenarios analysis,finding analysis and many combinations among them.In the open literature there have been reported interesting and signi ficant studies about HAZOP,like HAZOP and HAZAN differences (Gujar,1996)where HAZOP was identi fied as qualitative hazard identi fication technique,while HAZAN was considered for the quantitative risk determination.This difference is not strictly valid today,since there are now companies using HAZOP with risk analysis*Corresponding author.Tel.:þ525519442500x57043.E-mail addresses:mpmarin@imp.mx (M.Pérez-Marín),miguel.angel.rodriguezt@ ,matoral09@ (M.A.Rodríguez-Toral).Contents lists available at SciVerse ScienceDirectJournal of Loss Prevention in the Process Industriesjou rn al homepage :/locate/jlp0950-4230/$e see front matter Ó2013Elsevier Ltd.All rights reserved./10.1016/j.jlp.2013.03.008Journal of Loss Prevention in the Process Industries 26(2013)936e 940and its acceptance criteria(Goyal&Kugan,2012).Other approaches include HAZOP execution optimization(Khan,1997);the use of intelligent systems to automate HAZOP(Venkatasubramanian,Zhao, &Viswanathan,2000);the integration of HAZOP with Fault Tree Analysis(FTA)and with Event Tree Analysis(ETA)(Kuo,Hsu,& Chang,1997).According to CCPS(2001)any qualitative method for hazard evaluation applied to identify scenarios in terms of their initial causes,events sequence,consequences and safeguards,can beextended to register Layer of Protection Analysis(LOPA).Since HAZOP scenarios report are presented typically in tabular form there can be added columns considering the frequency in terms of order of magnitude and the probability of occurrence identified in LOPA.There should be identified the Independent and the non-Independent Protection Layers,IPL and non-IPL respec-tively.Then the Probability of Failure on Demand(PFDs)for IPL and for non-IPL can be included as well as IPL integrity.Another approach consists of a combination of HAZOP/LOPA analysis including risk magnitude to rank risk reduction actions (Johnson,2010),a general method is shown,without emphasizing in any particular application.An extended HAZOP/LOPA analysis for Safety Integrity Level(SIL)is presented there,showing the quan-titative benefit of applying risk reduction measures.In this way one scenario can be compared with tolerable risk criteria besides of being able to compare each scenario according to its risk value.A recent review paper has reported variations of HAZOP methodology for several applications including batch processes, laboratory operations,mechanical operations and programmable electronic systems(PES)among others(Dunjó,Fthenakis,Vílchez, &Arnaldos,2010).Wide and important contributions to HAZOP knowledge have been reported in the open literature that have promoted usage and knowledge of HAZOP studies.However,even though there is available the IEC standard on HAZOP studies,IEC-61882:2001there is not a worldwide agreement on HAZOP methodology and there-fore there exist a great variety of approaches for HAZOP studies.At international level there exist an ample number of ap-proaches in HAZOP studies;even though the best advanced prac-tices have been taken by several expert groups around the world, there is not uniformity among different consulting companies or industry internal expert groups(Goyal&Kugan,2012).The Mexican case is not the exception about this,but in the local oil and gas industry there exist a national PEMEX corporate standard that is specific in HAZOP application,it includes ranking risk scenarios (PEMEX,2008),qualitative hazard ranking,as well as the two ap-proaches recognized in HAZOP,Cause by Cause(CÂC)and Devia-tion by Deviation(DÂD).Published work including risk criteria include approaches in countries from the Americas,Europe and Asia(CCPS,2009),but nothing about Mexico has been reported.3.HAZOP variationsIn the technical literature there is no consensus in the HAZOP studies procedure,from the several differences it is consider that the more important are the variations according to:(DÂD)or (CÂC).Table1shows HAZOP variations,where(CQÂCQ)means Consequence by Consequence analysis.The implications of choosing(CÂC)are that in this approach there are obtained unique relationships of Consequences,Safeguards and Recommendations,for each specific Cause of a given Deviation. For(DÂD),all Causes,Consequences,Safeguards and Recommenda-tions are related only to one particular Deviation,thus producing that not all Causes appear to produce all the Consequences.In practice HAZOP approach(DÂD)can optimize analysis time development.However,its drawback comes when HAZOP includes risk ranking since it cannot be determined easily which Cause to consider in probability assignment.In choosing(CÂC)HAZOP there is no such a problem,although it may take more time on the analysis.The HAZOP team leader should agree HAZOP approach with customer and communicate this to the HAZOP team.In our experience factors to consider when choosing HAZOP approach are:1.If HAZOP will be followed by Layers of Protection Analysis(LOPA)for Safety Integrity Level(SIL)selection,then choose (CÂC).2.If HAZOP is going to be the only hazard identification study,it isworth to make it with major detail using(CÂC).3.If HAZOP is part of an environmental risk study that requires aConsequence analysis,then use(DÂD).4.If HAZOP is going to be done with limited time or becauseHAZOP team cannot spend too much time in the analysis,then use(DÂD).Although this is not desirable since may compro-mise process safety.Regarding risk ranking in HAZOP,looking at IEC standard(IEC, 2001)it is found that HAZOP studies there are(DÂD)it refers to (IEC,1995)in considering deviation ranking in accordance to their severity or on their relative risk.One advantage of risk ranking is that presentation of HAZOP results is very convenient,in particular when informing the management on the recommendations to be followedfirst or with higher priority as a function of risk evaluated by the HAZOP team regarding associated Cause with a given recommendation.Tables2and3are shown as illustrative example of the convenience of event risk ranking under HAZOP,showing no risk ranking in Table2and risk ranking in Table3.When HAZOP presents a list of recommendations without ranking,the management can focus to recommendations with perhaps the lower resource needs and not necessarily the ones with higher risk.Table1Main approaches in HAZOP studies.Source HAZOP approach(Crowl&Louvar,2011)(DÂD)(ABS,2004)(CÂC)&(DÂD)(Hyatt,2003)(CÂC),(DÂD)&(CQÂCQ) (IEC,2001)(DÂD)(CCPS,2008);(Crawley,Preston,& Tyler,2008)(DÂD),(CÂC)Table2HAZOP recommendations without risk ranking.DescriptionRecommendation1Recommendation2Recommendation3Recommendation4Recommendation5Table3HAZOP recommendations with risk ranking.Scenario risk DescriptionHigh Recommendation2High Recommendation5Medium Recommendation3Low Recommendation1Low Recommendation4M.Pérez-Marín,M.A.Rodríguez-Toral/Journal of Loss Prevention in the Process Industries26(2013)936e940937As can be seen in Tables 2and 3,for the management there will be more important to know HAZOP results as in Table 3,in order to take decisions on planning response according to ranking risk.4.HAZOP standard for the Mexican oil &gas industryLooking at the worldwide recognized guidelines for hazard identi fication (ISO,2000)there is mentioned that when consid-ering scenarios qualitative risk assignment,one may use risk matrix for comparing the importance of risk reduction measures of the different options,but there is not a speci fic risk matrix with risk values to consider.In Mexico there exist two national standards were tolerable and intolerable risk is de fined,one is the Mexican National Standard NOM-028(NOM,2005)and the other is PEMEX corporate standard NRF-018(PEMEX,2008).In both Mexican standards the matrix form is considered for relating frequency and consequences.Fig.1shows the risk matrix in (NOM,2005),nomenclature regarding letters in this matrix is described in Tables 4e 6.It can be mentioned that risk matrix in (NOM,2005)is optional for risk management in local chemical process plants.For Mexican oil &gas industry,there exist a PEMEX corporate standard (NRF),Fig.2,shows the corresponding risk matrix (PEMEX,2008).Nomenclature regarding letters in this matrix is described in Tables 7e 9for risk concerning the community.It is important to mention that PEMEX corporate standard considers environmental risks,business risks,and corporate image risks.These are not shown here for space limitations.The Mexican National Standard (NOM)as being of general applicability gives the possibility for single entities (like PEMEX)to determine its own risk criteria as this company opted to do.PEMEX risk matrix can be converted to NOM ’s by category ’s grouping infrequency categories,thus giving same flexibility,but with risk speci fic for local industry acceptance risk criteria.One principal consideration in ranking risk is to de fine if ranking is done before safeguards de finition or after.This de finition is relevant in:HAZOP kick-off presentation by HAZOP leader,explaining im-plications of risk ranking.HAZOP schedule de finition.Risk ranking at this point takes shorter time since time is not consumed in estimating risk reduction for each safeguard.If after HAZOP a LOPA is going to be done,then it should be advisable to request that HAZOP leader considers risk ranking before safeguards de finition,since LOPA has established rules in de fining which safeguards are protections and the given risk reduction.Otherwise if for time or resource limitations HAZOP is not going to be followed by LOPA,then HAZOP should consider risk ranking after safeguards de finition.Therefore,the HAZOP leader should explain to the HAZOP team at the kick-off meeting a concise explanation of necessary considerations to identify safeguards having criteria to distinguish them as Independent Protection Layers (IPL)as well as the risk reduction provided by each IPL.In HAZOP report there should be make clear all assumptions and credits given to the Protections identi fied by the HAZOP team.Figs.3and 4,shows a vision of both kinds of HAZOP reports:For the case of risk ranking before and after safeguards de finition.In Figs.3Fig.1.Risk matrix in (NOM,2005).Table 5Probability description (Y -axis of matrix in Fig.1)(NOM,2005).Frequency Frequency quantitative criteria L41in 10years L31in 100years L21in 1000years L1<1in 1000yearsTable 6Risk description (within matrix in Fig.1)(NOM,2005).Risk level Risk qualitative descriptionA Intolerable:risk must be reduced.B Undesirable:risk reduction required or a more rigorous risk estimation.C Tolerable risk:risk reduction is needed.DTolerable risk:risk reduction not needed.Fig.2.Risk matrix as in (PEMEX,2008).Table 7Probability description (Y -axis of matrix in Fig.2)(PEMEX,2008).Frequency Occurrence criteria Category Type Quantitative QualitativeHighF4>10À1>1in 10yearsEvent can be presented within the next 10years.Medium F310À1À10À21in 10years e 1in 100years It can occur at least once in facility lifetime.LowF210À2À10À31in 100years e 1in 1000years Possible,it has never occurred in the facility,but probably ithas occurred in a similar facility.Remote F1<10À3<1in 1000years Virtually impossible.It is norealistic its occurrence.Table 4Consequences description (X -axis of matrix in Fig.1)(NOM,2005).Consequences Consequence quantitative criteriaC4One or more fatalities (on site).Injuries or fatalities in the community (off-site).C3Permanent damage in a speci fic Process or construction area.Several disability accidents or hospitalization.C2One disability accident.Multiple injuries.C1One injured.Emergency response without injuries.M.Pérez-Marín,M.A.Rodríguez-Toral /Journal of Loss Prevention in the Process Industries 26(2013)936e 940938and4“F”means frequency,C means consequence and R is risk as a function of“F”and“C”.One disadvantage of risk ranking before safeguards definition is that resulting risks usually are found to be High,Intolerable or Unacceptable.This makes difficult the decision to be made by the management on what recommendations should be carried outfirst and which can wait.One advantage in risk ranking after safeguards definition is that it allows to show the management the risk scenario fully classified, without any tendency for identifying most risk as High(Intolerable or Unacceptable).In this way,the management will have a good description on which scenario need prompt attention and thus take risk to tolerable levels.There is commercial software for HAZOP methodology,but it normally requires the user to use his/her risk matrix,since risk matrix definition represents an extensive knowledge,resources and consensus to be recognized.The Mexican case is worldwide unique in HAZOP methodology, since it uses an agreed and recognized risk matrix and risk priori-tizing criteria according to local culture and risk understanding for the oil&gas sector.The risk matrix with corresponding risk levels took into account political,economical and ethic values.Advantages in using risk matrix in HAZOP are:they are easy to understand and to apply;once they are established and recognized they are of low cost;they allow risk ranking,thus helping risk reduction requirements and limitations.However,some disad-vantages in risk matrix use are:it may sometimes be difficult to separate frequency categories,for instance it may not be easy to separate low from remote in Table7.The risk matrix subdivision may have important uncertainties,because there are qualitative considerations in its definition.Thus,it may be advantageous to update Pemex corporate HAZOP standard(PEMEX,2008)to consider a6Â6matrix instead of the current4Â4matrix.5.ConclusionsHAZOP studies are not a simple procedure application that as-sures safe Process systems on its own.It is part of a global design cycle.Thus,it is necessary to establish beforehand the HAZOP study scope that should include at least:methodology,type(CÂC,DÂD, etc.)report format,acceptance risk criteria and expected results.Mexico belongs to the reduced number of places where accep-tance risk criteria has been explicitly defined for HAZOP studies at national level.ReferencesABS.(2004).Process safety institute.Course103“Process hazard analysis leader training,using the HAZOP and what-if/checklist techniques”.Houston TX:Amer-ican Bureau of Shipping.CCPS(Center for Chemical Process Safety).(2001).Layer of protection analysis: Simplified process risk assessment.New York,USA:AIChE.CCPS(Center for Chemical Process Safety).(2008).Guidelines for hazard evaluation procedures(3rd ed.).New York,USA:AIChE/John Wiley&Sons.CCPS(Center for Chemical Process Safety).(2009).Guidelines for Developing Quan-titative Safety Risk Criteria,Appendix B.Survey of worldwide risk criteria appli-cations.New York,USA:AIChE.Crawley,F.,Preston,M.,&Tyler,B.(2008).HAZOP:Guide to best practice(2nd ed.).UK:Institution of Chemical Engineers.Crowl,D.A.,&Louvar,J.F.(2011).Chemical process safety,fundamentals with ap-plications(3rd ed.).New Jersey,USA:Prentice Hall.Table8Consequences description(X-axis of matrix in Fig.2)(PEMEX,2008).Event type and consequence categoryEffect:Minor C1Moderate C2Serious C3Catastrophic C4 To peopleNeighbors Health and Safety.No impact on publichealth and safety.Neighborhood alert;potentialimpact to public health and safety.Evacuation;Minor injuries or moderateconsequence on public health and safety;side-effects cost between5and10millionMX$(0.38e0.76million US$).Evacuation;injured people;one ormore fatalities;sever consequenceon public health and safety;injuriesand side-consequence cost over10million MX$(0.76million US$).Health and Safetyof employees,serviceproviders/contractors.No injuries;first aid.Medical treatment;Minor injurieswithout disability to work;reversible health treatment.Hospitalization;multiple injured people;total or partial disability;moderate healthtreatment.One o more fatalities;Severe injurieswith irreversible damages;permanenttotal or partial incapacity.Table9Risk description(within matrix in Fig.2)(PEMEX,2008).Risk level Risk description Risk qualitative descriptionA Intolerable Risk requires immediate action;cost should not be a limitation and doing nothing is not an acceptable option.Risk with level“A”represents an emergency situation and there should be implements with immediate temporary controls.Risk mitigation should bedone by engineered controls and/or human factors until Risk is reduced to type“C”or preferably to type“D”in less than90days.B Undesirable Risk should be reduced and there should be additional investigation.However,corrective actions should be taken within the next90days.If solution takes longer there should be installed on-site immediate temporary controls for risk reduction.C Acceptablewith control Significant risk,but can be compensated with corrective actions during programmed facilities shutdown,to avoid interruption of work plans and extra-costs.Solutions measures to solve riskfindings should be done within18months.Mitigation actions should focus operations discipline and protection systems reliability.D ReasonablyacceptableRisk requires control,but it is of low impact and its attention can be carried out along with other operations improvements.Fig.3.Risk ranking before safeguard definition.Fig.4.Risk ranking after safeguards definition.M.Pérez-Marín,M.A.Rodríguez-Toral/Journal of Loss Prevention in the Process Industries26(2013)936e940939Dunjó,J.,Fthenakis,V.,Vílchez,J.A.,&Arnaldos,J.(2010).Hazard and opera-bility(HAZOP)analysis.A literature review.Journal of Hazardous Materials, 173,19e32.Goyal,R.K.,&Kugan,S.(2012).Hazard and operability studies(HAZOP)e best practices adopted by BAPCO(Barahin Petroleum Company).In Presented at SPE middle east health,safety,security and environment conference and exhibition.Abu Dhabi,UAE.2e4April.Gujar,A.M.(1996).Myths of HAZOP and HAZAN.Journal of Loss Prevention in the Process Industry,9(6),357e361.Hyatt,N.(2003).Guidelines for process hazards analysis,hazards identification and risk analysis(pp.6-7e6-9).Ontario,Canada:CRC Press.IEC.(1995).IEC60300-3-9:1995.Risk management.Guide to risk analysis of techno-logical systems.Dependability management e Part3:Application guide e Section 9:Risk analysis of technological systems.Geneva:International Electrotechnical Commission.IEC.(2001).IEC61882.Hazard and operability studies(HAZOP studies)e Application guide.Geneva:International Electrotechnical Commission.ISO.(2000).ISO17776.Guidelines on tools and techniques for hazard identification and risk assessment.Geneva:International Organization for Standardization.Johnson,R.W.(2010).Beyond-compliance uses of HAZOP/LOPA studies.Journal of Loss Prevention in the Process Industries,23(6),727e733.Khan,F.I.(1997).OptHAZOP-effective and optimum approach for HAZOP study.Journal of Loss Prevention in the Process Industry,10(3),191e204.Kuo,D.H.,Hsu,D.S.,&Chang,C.T.(1997).A prototype for integrating automatic fault tree/event tree/HAZOP puters&Chemical Engineering,21(9e10),S923e S928.Lawley,H.G.(1974).Operability studies and hazard analysis.Chemical Engineering Progress,70(4),45e56.Mannan,S.(2012).Lee’s loss prevention in the process industries.Hazard identifica-tion,assessment and control,Vol.1,3rd ed.,Elsevier,(pp.8e31).NOM.(2005).NOM-028-STPS-2004.Mexican National standard:“Norma Oficial Mexicana”.In Organización del trabajo-Seguridad en los procesos de sustancias químicas:(in Spanish),published in January2005.PEMEX.(2008).Corporate Standard:“Norma de Referencia NRF-018-PEMEX-2007“Estudios de Riesgo”(in Spanish),published in January2008. Venkatasubramanian,V.,Zhao,J.,&Viswanathan,S.(2000).Intelligent systems for HAZOP analysis of complex process puters&Chemical Engineering, 24(9e10),2291e2302.M.Pérez-Marín,M.A.Rodríguez-Toral/Journal of Loss Prevention in the Process Industries26(2013)936e940 940。

AForge中⽂⽂档教学⽂案A F o r g e中⽂⽂档AForgeAForge命名空间是/doc/1e88f362864769eae009581b6bd97f192279bf9b.html 框架，它包含框架和类的其他命名空间所使⽤的核⼼类，可以独⽴地⽤于各种⽬的。

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