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基于模糊层次分析法的课程思政效果评价——以工程热力学为例基于模糊层次分析法的课程思政效果评价——以工程热力学为例引言：随着社会的发展，培养高素质、全面发展的人才已经成为高等教育的主要任务之一。
而思想政治教育，作为高等教育的重要组成部分，对学生的思想道德素质和综合能力的培养起到了不可替代的作用。
因此，如何评价课程思政中的教学效果，对于进一步完善教育质量管理体系，提高思政教育有效性具有重要意义。
本文以工程热力学课程为例，采用模糊层次分析法对课程思政效果进行评价，并分析结果。
一、模糊层次分析法的基本原理模糊层次分析法是一种系统、综合性的分析决策方法，适用于解决一些多因素、多目标、模糊性较强的问题。
其基本原理是通过构建模糊层次结构，将主观判断转化为数值，从而实现对各因素的排序和评价。
模糊层次分析法包括建立层次结构模型、构建模糊判断矩阵、计算权重向量和模糊一致性检验等步骤。
二、工程热力学课程思政效果评价指标体系构建针对工程热力学课程，本文构建了包括“思政内涵”、“思政目标”、“教学过程”和“学生综合素质”在内的四个层次的评价指标体系。
其中，“思政内涵”包括爱国主义、集体主义、科学精神、人文关怀等方面的内容，“思政目标”包括道德修养、社会责任、科技创新等方面的目标，“教学过程”包括教学方法、教材内容、课程设置等方面的因素，“学生综合素质”包括思维能力、沟通能力、创新能力等方面的素质。
在构建评价指标体系时，我们充分考虑了工程热力学这门课程独特的学科特点和思政教育的目标要求。
三、模糊层次分析法的应用1. 构造模糊判断矩阵在模糊层次分析法中，模糊判断矩阵是对各指标之间相对重要性的判断矩阵。
通过专家讨论和问卷调查，我们将构造出对应于评价指标体系的模糊判断矩阵。
2. 计算权重向量在获得模糊判断矩阵后，通过计算权重向量，可以得到各评价指标的权重。
本文采用模糊特征向量法计算权重向量，得到每个指标相对于上一级指标的权重。
3. 模糊一致性检验为了验证模糊判断矩阵的合理性和一致性，采用一致性指标λ和平均随机一致性指标CR进行一致性检验。
模糊综合评价方法及其应用研究一、本文概述本文旨在探讨模糊综合评价方法及其应用研究。
我们将对模糊综合评价方法进行概述，阐述其基本原理和特点。
接着，我们将深入探讨模糊综合评价方法在各种领域中的应用，包括但不限于企业管理、环境评估、医疗卫生等。
通过对实际案例的分析，我们将展示模糊综合评价方法在解决实际问题中的有效性和实用性。
我们还将对模糊综合评价方法的未来发展进行展望，以期为其在更多领域的应用提供参考和借鉴。
通过本文的研究，我们希望能够为相关领域的研究者和实践者提供有益的启示和帮助。
二、模糊综合评价方法理论基础模糊综合评价方法（Fuzzy Comprehensive Evaluation，简称FCE）是一种基于模糊数学理论的评价方法，旨在解决那些难以用精确数学语言描述的问题。
这种方法最早由我国学者汪培庄于1983年提出，现已在多个领域得到了广泛应用。
模糊综合评价方法理论基础主要包括模糊集合理论、模糊运算规则和模糊关系矩阵。
其中，模糊集合理论是该方法的核心。
它允许在元素对集合的隶属程度不唯不精确的情况下进行定量描述，从而突破了传统集合理论中元素对集合的隶属关系必须明确的限制。
在模糊综合评价中，评价对象通常被视为一个模糊集合，而评价因素则构成该集合的多个子集。
每个子集都有一个隶属函数，该函数描述了评价对象在不同因素下的隶属程度。
通过对隶属函数进行计算和分析，可以得出评价对象在各个因素上的综合评价结果。
模糊运算规则是模糊综合评价方法的另一个重要组成部分。
它定义了模糊集合之间的运算方式，如并、交、补、差等，使得我们能够根据实际需求进行模糊集合的组合和转换。
模糊关系矩阵则用于描述评价对象与评价因素之间的模糊关系。
该矩阵中的元素表示评价对象在不同因素上的隶属度，是进行模糊综合评价的重要依据。
模糊综合评价方法理论基础包括模糊集合理论、模糊运算规则和模糊关系矩阵。
这些理论和方法为我们在复杂系统中进行综合评价提供了有效的工具。
几种模糊多属性决策方法及其应用一、本文概述随着信息时代的快速发展，决策问题日益复杂，涉及的属性越来越多，决策信息的不确定性也越来越大。
在这种背景下，模糊多属性决策方法应运而生，成为解决复杂决策问题的重要工具。
本文旨在探讨几种典型的模糊多属性决策方法，包括模糊综合评价法、模糊层次分析法、模糊集结算子等，并分析它们在实际应用中的优势和局限性。
本文首先介绍了模糊多属性决策方法的基本概念和理论基础，为后续研究提供必要的支撑。
接着，详细阐述了三种常用的模糊多属性决策方法，包括它们的原理、步骤和应用范围。
在此基础上，通过案例分析，展示了这些方法在实际应用中的具体运用和取得的效果。
通过本文的研究，读者可以深入了解模糊多属性决策方法的原理和应用，掌握其在实际问题中的使用技巧，为解决复杂决策问题提供有力支持。
本文也为进一步研究和改进模糊多属性决策方法提供了参考和借鉴。
二、模糊多属性决策方法概述模糊多属性决策（Fuzzy Multiple Attribute Decision Making，FMADM）是一种处理不确定性、不精确性和模糊性的决策分析方法。
在实际问题中，由于信息的不完全、知识的局限性或环境的动态变化，决策者往往难以获取精确的属性信息和权重信息，这使得传统的多属性决策方法难以应用。
模糊多属性决策方法通过引入模糊集理论，能够更好地处理这种不确定性和模糊性，为决策者提供更合理、更可靠的决策支持。
模糊多属性决策方法的核心思想是将决策问题中的属性值和权重视为模糊数，利用模糊集理论中的运算法则进行决策分析。
根据不同的决策目标和背景，模糊多属性决策方法可以分为多种类型，如模糊综合评价、模糊多目标决策、模糊群决策等。
这些方法在各自的领域内都有着广泛的应用，如企业管理、项目管理、环境评估、城市规划等。
在模糊多属性决策方法中，常用的模糊数有三角模糊数、梯形模糊数、正态模糊数等。
这些模糊数可以根据实际问题的需要选择合适的类型，以更好地描述属性值的不确定性和模糊性。
模糊层次分析法模糊层次分析法是一种多变量决策分析方法，旨在帮助决策者在复杂的决策问题中做出合理的选择。
与传统的层次分析法相比，模糊层次分析法能够处理不确定性、模糊性和主观性的问题，因此在实际应用中具有很高的灵活性和适应性。
模糊层次分析法的核心思想是将问题拆解为不同的层次结构，分别从不同角度对问题的因素进行评价和排序。
具体来说，模糊层次分析法包括以下几个步骤：定义目标层、准则层和方案层，建立层次结构模型；构建模糊层次判断矩阵，利用专家经验和模糊数学的方法对层次结构中的评价指标进行两两比较，得到判断矩阵；计算模糊一致性指标，判断判断矩阵的一致性程度；通过模糊层次权重计算方法将判断矩阵转化为权重向量，评估和排序方案。
首先，模糊层次分析法要明确问题的目标。
目标层是决策问题的最高层，是整个层次结构的根节点。
目标层定义了决策问题的目标和愿景，可以是一个具体的指标，也可以是一项重要的战略目标。
例如，对于一个公司来说，提高市场份额、提升产品质量和降低成本可能是目标层的几个重要目标。
其次，确定准则层。
准则层是指对于实现目标所需要的关键因素或评价标准。
准则层的每个因素都与目标层直接相关，通过对准则的评估和排序可以帮助决策者识别出最为关键的因素。
在确定准则层时，应该考虑因素之间的相互关联性和重要性。
最后，定义方案层。
方案层是指为实现目标而采取的具体措施或方案。
一般情况下，方案层是决策问题的最低层。
在定义方案层时，应该考虑到各个方案之间的可行性、资源需求和可能的风险。
在模糊层次分析法中，决策者需要对准则层和方案层中的因素进行两两比较，构建模糊判断矩阵。
模糊判断矩阵是用来描述不确定和模糊的评价值的，可以通过专家判断、模糊数学方法和模糊逻辑推理进行计算和推断。
模糊判断矩阵的元素通常采用模糊数表示，模糊数由隶属函数和隶属度组合而成。
在模糊层次分析法中，为了判断判断矩阵的一致性程度，需要计算模糊一致性指标。
模糊一致性指标能够量化判断矩阵的一致性程度，判断决策者所提供的判断是否存在矛盾和不一致的情况。
三标度模糊层次分析法的应用探析桥梁在现代交通运输中应用比较广泛，是一种运输枢纽，可以有效促进国民经济增长以及社会生活水平的提高。
为了保证桥梁的安全运行，必须要建立完善的桥梁安全评估体系。
1、国内外桥梁安全评估的研究现状国外的桥梁安全主要集中在对安全风险的数值模拟以及实验分析上，缺少桥梁安全评估体系的研究[1]。
我国的桥梁安全评估技术也得到了广泛的发展。
部分学者主张通过分析典型桥梁事故特点，指出桥梁安全事业应该注重在事故预防措施上。
本文提出的研究方法，是考虑到桥梁安全评估本身所具有的复杂性、模糊性以及多样性等特点，提出了一种结合三维度层次分析法以及模糊判断法的集合方法，可以有效提高评价指标判断的准确度，减少重复检验过程。
这种三标度模糊层次分析法具有客观性的特点，可以有效避免主观性带来的偏差，同时在计算上，也比价方便，避免大量计算[2]。
层次分析法是一种定性和定量相结合的、系统化的、层次化的分析方法。
使用层次分析法将桥梁安全性的指标确定下来，利用三标度当做层次评价指标比率标度，建设成比较矩阵。
利用矩阵计算出评价指标的权重，使用模糊综合评判模型，判断出桥梁的安全等级，为桥梁的安全管理以及维修加固等工作提供数据参考。
2、桥梁安全状况的评判对桥梁的综合状态进行安全评估，必须要建立评价指标体系的结构模型。
依据《公路桥梁技术评定标准》以及《公路桥涵养护规范》，桥梁的评估指标应该分为上下结构以及桥面三种层面[3]。
同时依据相关文献，将桥梁的安全评定等级划分为五个级别（如表1所示）。
并根据相关文献，将各个级别的相应指标区间赋予出来。
3、桥梁安全评价的指标权重的确定对桥梁的安全状况进行模糊综合评判中，比较重要的一个环节便是确定其指标的权重，主要采用的权重判断方法为德尔菲法以及专家打分法。
3.1确定判断矩阵通过对同一层次的评价指标进行对比，得出比较矩阵。
比较矩阵建立的基础是《公路桥梁技术状况评定标准》以及相关专家建议。
基于模糊层次分析法的企业战略选择研究随着市场经济的发展，企业面对的竞争越来越激烈，企业战略的制定和实施成为企业成功的重要因素。
但是，在各种市场、技术、政策等因素的影响下，企业在制定战略时经常会面临多个不确定因素的干扰，这就需要企业在制定战略时充分考虑各种因素之间的相互影响和权衡。
模糊层次分析法是一种基于模糊数学理论的决策方法，可以帮助企业制定更为科学和合理的战略。
一、模糊层次分析法概述模糊层次分析法（Fuzzy Analytic Hierarchy Process，简称FAHP）是一种决策分析方法，可以将复杂的决策问题分解成几个层次，通过对因素权重的确定和综合评价，得出最终的决策结果。
FAHP的核心是模糊数学理论，在FAHP中，每个因素都被赋予一个模糊数，即人们主观上对该因素的认知程度。
模糊数的取值范围在[0,1]之间，越接近1表示越重要，越接近0表示越不重要。
这种模糊数学理论的灵活性，能够较好地处理多个因素之间的不确定性和复杂性。
二、模糊层次分析法在企业战略选择中的应用1.建立层次结构在FAHP中，首先需要将决策问题分解成一个多层次的层次结构，每一层对应着一个因素，包括目标层、准则层和方案层。
目标层是最高层，企业的整体目标和发展方向属于这一层，准则层是中间层，用于评价各种方案，方案层是最底层，对应着各种具体的策略方案。
2.构建判断矩阵在确定层次结构后，需要构建判断矩阵，对各因素之间的相对影响进行量化。
对于每一个判断矩阵，需要进行两两比较，用一个0~9的整数代表一组因素A与B的相对重要程度之间的模糊量化描述。
这个描述称为隶属函数，可以用图形方式表示。
3.计算权向量在判断矩阵构建完成后，需要计算各层次之间的权向量，即确定各层次之间的相对权重。
对于一次判断矩阵输入，计算各因素之间的权值向量，最终权值向量即为此次输入结果的权重。
4.实现综合评价在计算所需参数之后，就可以进行综合评价，得出最终的决策结果。
模糊层次分析法模糊层次分析法（Fuzzy Analytic Hierarchy Process，简称FAHP）是一种用于多标准决策的数学方法。
它结合了模糊逻辑和层次分析法（Analytic Hierarchy Process，简称AHP）的思想，能够处理模糊性和不确定性的问题。
FAHP在工程管理、经济决策、环境评估等领域具有广泛的应用。
FAHP的核心思想是将问题分解为多个层次，并对每个层次的因素进行比较和权重分配。
在FAHP中，通过模糊数来表示专家的判断和评价，并利用模糊数之间的运算进行计算。
模糊数是由一个值和一个隶属度函数组成的，可以用来表示各种可能性和不确定性。
FAHP的步骤包括：问题的层次划分、建立模糊判断矩阵、确定权重、计算总权重和一致性检验。
首先，将问题按照层次结构进行划分。
层次结构是由一系列目标、准则和方案组成的，目标是最终要达到的结果，准则是用于评价和选择方案的标准，方案是可供选择的备选方案。
然后，根据专家判断和评价，建立模糊判断矩阵。
模糊判断矩阵是由模糊数填充的矩阵，用于表示各个层次之间的相对重要性。
模糊判断矩阵的元素可以通过专家评价或统计数据得出。
接下来，确定权重。
根据模糊判断矩阵，可以计算得出每个层次因素的权重。
权重的计算可以利用模糊综合评判法，将模糊数进行聚合。
然后，计算总权重。
将各个层次因素的权重进行组合，得出各个方案的总权重。
最后，进行一致性检验。
通过计算一致性指标来判断判断矩阵的一致性。
一致性指标的计算可以利用随机一致性指标进行。
FAHP的优点是能够处理模糊性和不确定性，对专家判断和评价有较好的灵活性。
它还能够结合多个层次因素进行权衡，提高决策的科学性和准确性。
总之，FAHP是一种多标准决策方法，能够应对复杂的决策问题。
它的核心思想是将问题分解为多个层次，通过模糊数的运算进行计算和评估。
FAHP在实际应用中具有广泛的应用前景，可以帮助决策者做出科学、准确的决策。
模糊分析法案例模糊分析法是一种用于处理模糊信息的数学工具，它在实际问题中具有广泛的应用。
本文将以一个实际案例来介绍模糊分析法的应用，以帮助读者更好地理解这一方法的具体运用。
案例背景，某公司要进行市场调研，以确定新产品的定价策略。
市场调研结果显示，消费者对于该产品的价格存在一定的模糊性，即消费者对于产品价格的期望并不是一个确定的值，而是一个模糊的范围。
因此，公司需要利用模糊分析法来确定最合适的定价策略。
首先，我们需要建立模糊集合。
在这个案例中，我们可以将消费者对产品价格的期望划分为几个模糊集合，比如“低价”、“中等价”和“高价”。
然后，我们需要确定每个模糊集合的隶属度函数，即消费者对于每个价格区间的偏好程度。
通过调研数据，我们可以得到每个价格区间的隶属度函数。
接下来，我们需要进行模糊运算。
在确定定价策略时，我们可以利用模糊运算来对不同因素进行综合考虑。
比如，我们可以利用模糊加法和模糊乘法来确定最终的定价策略。
通过模糊加法，我们可以对不同因素的影响程度进行加权求和，得到一个综合的影响程度。
而通过模糊乘法，我们可以对不同因素的影响程度进行综合考虑，得到一个综合的影响程度。
最后，我们需要进行模糊推理。
在确定最终的定价策略时，我们需要利用模糊推理来得出最终的结论。
通过模糊推理，我们可以将模糊信息转化为确定的结论，从而确定最终的定价策略。
通过以上步骤，我们可以利用模糊分析法来确定最合适的定价策略，从而更好地满足消费者的需求，提高产品的市场竞争力。
总结，模糊分析法是一种处理模糊信息的有效工具，它在实际问题中具有广泛的应用。
通过以上案例的介绍，相信读者对于模糊分析法的应用有了更深入的理解。
在实际问题中，我们可以根据具体情况，灵活运用模糊分析法，从而更好地解决实际问题，提高决策的准确性和可靠性。
Possibilistic regression analysis of influential factors for occupational health and safety management systemsAzizul Azhar Ramli a ,⇑,Junzo Watada a ,Witold Pedrycz b ,caGraduate School of Information,Production and Systems,Waseda University,2-7Hibikino,Wakamatsu-ku,Kitakyushu-shi,Fukuoka-ken 808-0135,Japan bDepartment of Electrical &Computer Engineering,University of Alberta,Edmonton,Alberta,Canada T6G 2V4cSystems Research Institute,Polish Academy of Sciences,Warsaw,Polanda r t i c l e i n f o Article history:Available online 24March 2011Keywords:Intelligent data analysisOccupational health and safety management systemsPossibilistic regression analysisa b s t r a c tThe code of occupational health and safety (OHS)is an influential regulation to improve the on-the-job safety of employees.A number of factors influence the planning and implementation of OHS manage-ment systems (OHSMS).The evaluation of OHSMS practice is the most important component when form-ing a health and safety environmental policy for employees.The objective of this research is to develop an intelligent data analysis (IDA)in which possibilistic regression being endowed with a convex hull approach is used to support the analysis of essential factors that influence OHSMS.Given such subjective terms,the obtained samples can be conveniently regarded as fuzzy input/output data represented by membership functions.The study offers this vehicle of intelligent data analysis as an alternative to eval-uate the influential factors in a successful implementation of OHS policies and in this way decrease an overall computational effort.The obtained results show that several related OHSMS influential factors need to be carefully considered to facilitate a successful implementation of the OHSMS procedure.Ó2011Elsevier Ltd.All rights reserved.1.IntroductionIn the recent years,the implementation policy of occupational health and safety (OHS)becomes the major requirement to prepare and provide the best solution to assure health and safety in work-ing environment (Ayomoh and Oke,2006;Sgourou et al.,2010).There are two major groups,which directly involve this important regulation;that is employees’personnel and administrative staffs.The overall combination of OHS code ethics and activities has to be clearly defined and their results should be periodically evaluated through some OHS management system (OHSMS).In this situation,the evaluation of factors that influence an OHS provides a useful feedback to employees’personnel and administrative staff.This process may produce higher safety consciousness as well as con-tribute to the well-being in a workplace (Gallagher,2000;Hwang et al.,2009).In addition,the most essential albeit somewhat controversial point concerns a procedure on how to obtain sound knowledge re-lated to the OHS practices while dealing with imprecise or vague data.The inherent complexity of OHS stems from several sources.In particular,we need to stress that a simple computational ap-proach is often inadequate and traditional data about incidents/claims have also proved to be quite unreliable (Gallagher et al.,2003;Dul and Neumann,2009).In light of this,a genuine need emerges to develop an alternative approach,which enables us to analyze and provide high quality results for the continuous improvement of OHSMS implementation procedures (Gallagher et al.,2001).Currently,supervisors or auditors can use a number of instru-ments or audit tools in their evaluation of OHSMS influential fac-tors.The factors or criteria that affect OHS practices usually depend on company policy and regulations,where its evaluation process involves a number of approaches or/and parameters,which are often based on imprecise data (Watada et al.,1998).Be-sides that,some companies/organizations still use open-ended and somewhat subjective questions.These types of questions require some judgment process such as OHS experts’interpretation to ana-lyze and interpret the results.Without this,it is difficult to arrive at conclusive results or generate useful knowledge (Robson et al.,2005).Moreover,emerging Internet facilities offer advantages to the administration section in companies/organizations when developing a web portal for each level of employees to assess their administrative OHS ing this technology in place,related parties such as auditors,companies/organizations administration and employees can envision quite tangible benefits.In order to acquire benefits from the analysis of the results and facilitate their comprehensive interpretation related to the OHSMS implementation,an adequate analysis is badly needed.The main objective of this research is to employ possibilistic regression anal-ysis to the OHSMS evaluation.We anticipate that the possibilistic0925-7535/$-see front matter Ó2011Elsevier Ltd.All rights reserved.doi:10.1016/j.ssci.2011.02.014⇑Corresponding author.Tel.:+818039819429.E-mail addresses:azizulazhar@moegi.waseda.jp (A.A.Ramli),junzow@osb.att.ne.jp (J.Watada),pedrycz@ece.ualberta.ca (W.Pedrycz).regression analysis has the capability of producing a meaningful and noteworthy results related to the most influencing factor of successful OHSMS practice.The possibilistic regression is imple-mented with the hybrid approach,which involves a certain geo-metric concept called a convex hull approach,specifically a Beneath–Beyond algorithm(Ramli et al.,2009).This selected ap-proach is appropriate here because of its underlying efficiency and consistency while dealing with imprecise data.In addition, the possibilistic regression analysis enables us to determine and rank the factors that significantly influence the OHSMS practice among selected companies/organizations.This intelligent data analysis(IDA)has been selected because of its efficiency and consistency while dealing with imprecise input data such as in OHSMS evaluation practice,which closely link to the essence of human decision-making processes,especially when dealing with a large amount of fuzzy input–output data.As it will become revealed,this research leads us to an interesting and prac-tically relevantfinding that among six selected OHSMS influence factors,the three of them are highly ranked.By this means,compa-nies/organizations could manage their OHS policy implementation procedure by considering these important factors at some stage.The paper is organized as follows.In Section2,a pertinent liter-ature on OHS policy,its influential factors and the important and efficient performance of OHSMS are reviewed.A general outline of the possibilistic regression model and an overview of the convex hull based approach for possibilistic regression model are high-lighted here.Section3presents an analysis of implementation fac-tors that affect the planning and implementation of OHSMS,while Section4interprets the results of possibilistic regression models obtained in this way.Section5presents some concluding remarks.2.Occupational health and safety policy:a brief overviewCagno et al.(2010)revealed the identification of company occu-pational health and safety(OHS)related significant success factors and their interactions is a crucial task issue to better understand and examine on how improvement interventions impact on the OHS performance of the company.All employers are required un-der the OHS Act to accept the term of‘duty of care’for the health and safety of all people in workplace.Implementing this action means that everyone in workplace should be aware of potential hazards and take steps to protect workplaces from accidents,inju-ries,and illnesses(Hale,2003;van Rhijn et al.,2005;Drebit et al., 2010).Generally,OHS has become a common and important compa-nies/organizations code of ethics over the past20years.Closely re-lated to this distinct term is OHS Management System(OHSMS), which has been defined as‘‘a combination of the planning and review,the management organizational arrangements,the consulta-tive arrangement and the specific program elements that work together in an integrated way to improve health and safety perfor-mance’’(Gallagher et al.,2003).The OHSMS implementation is based on traditional OHS pro-grams and it commonly has been understood that OHSMS realiza-tion is more proactive,better internally integrated and evaluates those influential elements of this policy for realizing successfully continuous improvement procedure.Additionally,finding the agreement upon criteria being used to assess the effectiveness or methods of measurement and evaluation is especially difficult in cases when basic disagreement exists upon the priorities of influ-ential factors being considered.Basically,as general system theory and fundamental properties of the OHSMS clearly suggests,the general characteristics include OHSMS objective,OHSMS specification,relationship of the OHSMS to other systems and the OHSMS maintenance.Although OHS features as stated above are highly recommended,its realization results in a considerable diversity(John and Anthony,2001).Rob-son et al.present the basic conceptual framework underlying the review of OHSMS(Robson et al.,2005)as shown in Fig.1.With regard to Fig.1,we can note that thefinal outcomes were identified under consideration of the ultimate purpose of OHSMS Intervention phase.Therefore,this phase should be completed with anticipation that this would improve health and safety of many stakeholders,especially employees as well as administrative section.Furthermore,we should carefully pursue the initial phase, intervention phase,and implementation in order to fully optimize those outcomes.Considering this,efficient and proactive actions including analysis and interpretation of soundfindings should form one of the important steps.Additionally,related critical suc-cess factors should be clearly defined during this process and then related to the priority ranking of the general routine of OHSMS ap-proaches/components.These factors might change depending upon safety climate,employee knowledge and behavior,beliefs, perceptions and several other related factors including company background and government regulation on OHS(Bellamy et al., 2008;Caroly et al.,2010).2.1.Critical success factors of influential occupational health and safety policy implementationNowadays,the growing use of OHSMS shows both a choice of one kind of OHS intervention in preference to others and a signif-icant investment offinancial and human resources by both govern-ment and business(Gallagher et al.,2001).Therefore the needs for better management related to this policy position themselves on the agenda of most companies/organizations all around the world (Challis et al.,2005;Geldart et al.,2010).In general,OHS policy is one of a practice safety plan to provide and maintain a work envi-ronment safe and without risk for health(Matias and Coelho,2002; Papadopoulos et al.,2010;Robertson et al.,2008;Neumann et al., 2009).Frick et al.in2000stated that around the world OHSMS has globally evolved the major strategy to reduce the serious social and economic problem of ill health in the working area(Robson et al.,2005;Derosier et al.,2008).Therefore,the lack of consideringA.A.Ramli et al./Safety Science49(2011)1110–11171111this critical issue will lead to major problems,especially related to employee’s health and safety(LaMontagne et al.,2004).Much of related research is not directly concerned with OHSMS –it merely implies that certain factors or aspects of an OHSMS ex-hibit positive effects on OHSMS action policy and its implementa-tion procedure(Thanet and Hadikusumoa,2008).Highlighted as the most valuablefindings in OHSMS,Gallagher (2000)support the conclusion that a particular type of OHSMS called‘adaptive hazard managers’distinguished by a‘safe place’control strategy and‘innovative management structure/style’per-forms better than other types,especially‘unsafe act minimizes’with a‘safe person/traditional management’approach(Robson et al.,2005).Several related literature studies on OHSMS indicate that a set of six key variables that should be periodically considered includes the following:i.Development of an OHS policy and program.ii.Method of OHSMS consultation sessions.iii.Setting up a OHSMS training strategy.iv.Setting up hazard identification and workplace assessmentprocess.v.Development and implement of OHSMS risk control strategies.vi.Promoting,maintaining and improving of OHSMS strategies.These points have been devised to help companies/organiza-tions implement efficient and effective OHSMS,which facilitated the prevention of accidents,incidents,injuries and work-related ill-health(Parker et al.,2006;Paul and Maiti,2008).Moreover, these dangerous situations are not avoidable and some of them may be repetitive because of the differences among workplaces (Leclercq et al.,2007;Grassi et al.,2009).Therefore,an efficient approach becomes our major concern in order to rank OHSMS influential factors.Currently,the general the-ory of OHS and OHSMS is used in most of the companies/organiza-tions all around the world to successfully implement this policy.As mentioned in the previous section,the requirements of an IDA tool are faced with a large size of OHSMS samples and therefore a way of dealing with imprecise data presentation becomes necessary (Moriyama and Ohtania,2009).2.2.The importance of occupational health and safety policy assessment procedureIn general,the International Labour Organization(ILO)has stressed that when practical ergonomics approaches are built in the workplaces environment and participatory training methods are engaged,the approaches have been proven useful for facilitat-ing concrete workplace improvements under the existing condi-tions present in developing countries(Kawakami and Kogi,2005; Niu,2010).In addition to this broad set of OHS significant needs,Zink in 2005highlighted the assessment of OHSMS influential factors be-comes a preliminary phase because of the following reasons:i.Prevention and systematic approaches.ii.Continuous improvement.iii.Integration in normal operations and planning.prehensive deployment.v.Strong relationship to policy and strategy and respective goals.vi.Orientation toward the best in class(benchmarking).Moreover,applying ergonomic principles such as OHS policy is beneficial to the workers as well as employers.Both parties are equally significant(Niu,2010).In addition,healthy employees can be nearly three times more productive than those being of poor health.Niu has also composed the potential effects of ignoring OHS procedure by both workers and employers,refer to Table1.Consequently,on the basis of above-listed reasons,we can real-ize here that good quality and highly accurate results are required in order to clearly determine appropriate OHSMS influential fac-tors,which were acknowledged as a major component of OHS pol-icy.Moreover,a suitable timeline becomes an important issue because it is interrelated with the frequency of analysis being made.Therefore,a real-time data analysis looks more appropriate to efficiently deal with this critical problem;likewise,an adequate IDA tool is also necessitated.Overall,considering future trends of the OHSMS data analysis, one should emphasize that here we are faced with large scale data, which come from various sources and of different formats.There-fore,the needs of robust IDA become of priority given that such analysis is capable of producing optimized results within some gi-ven time constraints.3.Fundamental ideas of models of possibilistic regressionIn statistical regression,deviations between observed and esti-mated values are assumed to be due to random errors.Although conventional regression has been applied to various areas,the re-lated problems include the vague relationship existing between in-put and output variables that cannot be clearly justified(Ciarapica and Giacchetta,2009).Therefore,this becomes a major reason be-hind its unsuccessful usage in the meaningful interpretation of the model.Regression analysis is one of commonly encountered ap-proaches in describing relationships among the analyzed data. The regression models explain dependencies between independent and dependent variables.The variables,which are used to explain the other variable(s)are called explanatory ones(Watada and Ped-rycz,2008).A‘‘standard’’numeric linear regression model comes in the following formy¼a0þa1x1þÁÁÁþa K x K:ð1ÞAs an interesting and useful extension,Tanaka et al.(1982) introduced an enhancement of the regression model by accommo-dating fuzzy sets thus giving rise to possibilistic regression.The models of this category reflect upon the fuzzy set based nature of relationships between the dependent and independent variables. Table1Potential effects of ignoring OHS policy procedure(Niu,2010).Workers EmployersPain and suffering due to injuries andoccupational diseasesIncreased absenteeism and lostworking timeMedical care cost Adverse effects on labor relations Lost work time Higher insurance and compensationcostsLost future earning and fringebenefitsIncreased probability of accidentsand errorsReduced job security and careeradvancementRestriction,job transfer and higherturnover of workers Lost home production and child care Scrap and decreased productionHome care costs provided by familymembersLawsuitsAdverse effects on family relations Low-quality workLost sense of self-worth and identity Less spare capacity to deal withemergenciesAdverse effects on social andcommunity relationshipsHigh administrative and personnelcostsAdverse effects on recreationalactivities1112 A.A.Ramli et al./Safety Science49(2011)1110–1117The upper and lower regression boundaries of the possibilistic regression are used to quantify the possibilistic distribution of the output values.As an alternative to the possibilistic specification,an inexact relationship among those dependent and independent variables can be represented via fuzzy linear regression expressed in the fol-lowing form:e Y¼e A0X0þe A1X1þÁÁÁþe A K X K¼e AX t;ð2Þwhere X=[X0,X1,...,X K]is a vector of independent variables;e A¼½e A0;e A1;ÁÁÁe A K is a vector of fuzzy coefficients represented in the form of symmetric triangular fuzzy numbers and denoted by e A j¼ða j;c jÞ.The membership function of the fuzzy number is de-scribed in the form:u~ A j ða jÞ¼1Àj a jÀa j jj;if c j–0;a jÀc j6a j6a jþc j1;if c j¼0;a j¼a j0;otherwise8>><>>:ðj¼0;...;KÞð3Þwhere a j and c j are the central(modal)value and the spread of the triangular fuzzy number,respectively.Additionally,possibilistic regression becomes the possibilistic model that can be used in the context of possibility theory to provide a new methodology for cap-turing vague and incomplete knowledge(Ramli et al.,2009).3.1.Convex hull based approach for possibilistic regression modelAs already noted,the membership functions of fuzzy numbers can be calculated quite easily if each fuzzy coefficient is specified by some parameterized membership function of a certain form (Hong et al.,2001).Apart from that,the main problem here is about an estimation of the regression coefficients and completing subsequent prediction within the framework of the fuzzy environ-ment.There are two reasons behind that.In general,we may encounter a large number of data.Furthermore,by considering the discussed format of fuzzy data in the resulting analysis we may be faced with a certain level of difficulty.Let us consider a problem,which concerns n samples and K in-put attributes(variables)of the fuzzy numbers.When we calculate the product of unknown fuzzy parameters and given fuzzy data, the straightforward computing method would be to take all verti-ces of the fuzzy data into consideration without separating them into various cases based upon the sign of the fuzzy data and the sign of the unknown fuzzy parameters.An additional difficulty arises because of the appearance of nÃ2K products of fuzzy num-bers(Watada et al.,2009).In light of the associated computing overload,the implementation of LP becomes impossible and we need to look at some other reasonable optimization alternative. Fig.2illustrates an example of rectangles,which are the loci of the membership’s functions of fuzzy data.Due to the inherently granular nature of the processed data(re-fer to the rectangular shapes illustrated in Fig.2)each of points there can represent the locus of the graphs of the corresponding membership function.Hence,the implementation of IDA approach solution is obtained by considering all the locus points of the ana-lyzed sample.Considering the outside points(locus points),which were constructed during the previous process,results in the adap-tation of a convex hull approach.The vertex points of selected loci will become possible convex vertices and these points will connect to each other to form convex hull edges or boundaries.In the se-quel,the connected edges will construct a convex hull for selected samples of fuzzy data and basically,whole of analyzed data will fall inside the constructed convex hull.The essence of the process is illustrated in Fig.3.Therefore,based on the developed convex hull,the determina-tion of the possibilistic regression to represent the distribution of sample data becomes easier because slight changes(either decreasing or increasing)of the vertex points influence the model and these points(that is the vertex points of only selected loci) must be considered for further LP formulation.In other words, we just consider selected vertex points in the analysis,which pre-viously resulted in building up the convex hull structure.Based on the original method of the determination of the con-vex hull,the process has to be realized using all given samples.The IDA algorithm consists of the following steps:Step_1:Load a set of fuzzy data samples(OHSMSrelated experimental data)Step_2:Perform fuzzy number optimization processfor obtaining the total product of fuzzynumbers,nÂ2KStep_3:Determine the outsider vertex points givenas the loci of the membership functions’graphsStep_4:Perform the Beneath–Beyond algorithm toformulate the convex hull,H0,using one ofthe selected vertex points that were chosenfor building the convex hullSubstep_4.1:Connect each of the selected potential vertexpoints to construct convex edgesSubstep_4.2:Connect constructed edges to createboundaries of a convex hull,H bSubstep_4.3:Omit points that are not included in theconvex hull,H bStep_5:Newly arrived data added to the initialanalyzed sample of dataA.A.Ramli et al./Safety Science49(2011)1110–11171113Step_6:Newly added sample data are too large or processing time is adequate?If Yes move to Step_2otherwise proceed to Step_7Step_7:Output the solution and terminate the processRamli et al.highlighted that the choice of the Beneath–Beyond algorithm as a convex hull approach is legitimate here considering that no extra computing is required for the construction of the fa-cet structure,which may reduce the computational time required to obtain the best solution for an equivalent problem.4.A determination of occupational health and safety management system influential factorsHere,we present an analysis realization related with OHSMS,which focuses on factors influencing the successful planning and implementation for OHSMS.We use selected samples of fuzzy I/O data coming from a certain number of companies/organiza-tions,which fully performed and successfully implemented the OHSMS policy.Moreover,those selected companies/organizations are coming from similar business type,working environment and culture as well as administrative and workers population (up to 90–95%of similarity).In this setting,we discuss the efficiency of the method of constructing a possibilistic regression for the OHSMS fuzzy data.The overall flow of the processing is illustrated in Fig.4.The selected samples come from 200companies/organizations in Malaysia,which evaluated their OHSMS influential factors arriv-ing at six inputs and a single output variable,see Table 2.These samples of data are gathered from non-government organization (NGO)cooperated with the Department of Occupational Safety and Health (DOSH)under the Ministry of Human Resource inMalaysia.This NGO focuses on monitoring of OHS policy practices in Malaysian companies/organizations.The size of each company/organization is around 1500employees including administrative personnel.In addition,these OHSMS related data are collected in 2008.Moreover,the NGO accumulates collects raw data from more than 5000companies/organizations in every 6months.Based on these variables,the data are represented as fuzzy (lin-guistic)terms such as ‘unsatisfactory’,‘satisfactory’,‘good’,‘very good’and ‘excellent’.This format of data becomes fully justifiable due to the unavailability of detailed numeric assessments.Table 3illustrates several some sample data considered in this problem.Here K =6input attributes (variables)where the number of data,n ,is equal to 200.Therefore,the overall number of the vertices of the fuzzy num-bers is n Ã2K =200Ã26=12,800.Both the response (dependent)and explanatory (independent)attributes (variables)are repre-sented as asymmetrical triangular fuzzy numbers,A =(l ,c ,r ).Note that,c is called the center of A and l =c Àn and r =c +#are called the left and right end points,respectively.Considering the first company,Comp001;for OHSPP attribute,related inputs represent the fuzzy number as (0.10,0.56,0.90),see Table 3.This input isTable 2OHSMS related input and output variables describing 200selected companies/organizations.No.Variables1.Inputs~a 1OHSPPDevelop an OHS policy and program 2.~a 2OHSCS Method of OHSMS consultation sessions 3.~a 3OHSTS Set up an OHSMS training strategy4.~a 4OHSHA Set up hazard identification and workplace assessment process5.~a 5OHSRC Develop and implement OHSMS risk control strategies6.~a6OHSPM Promote,maintain and improve OHSMS strategies7.Output OHSEIEfficiency of OHSMS implementation1114 A.A.Ramli et al./Safety Science 49(2011)1110–1117described as(l,c,r).In addition,n and#assume the values0.46and 0.34,respectively;refer to Fig.5.We constructed the possibilistic regression model to represent the OHSMS influential factors for200selected companies/organi-zations and obtained the possibilistic regression coefficients, ~a6;~a5;~a4;~a3;~a2;~a1and~a0,see Table4.Each of the regression coeffi-cients represents a fuzzy parameter~a j¼ðm j;c jÞdescribed as a symmetric triangular membership function with center,m j and fuzzy half-width(spread),c j.The objective of LP is to determinethe lower and upper limits of the fuzzy coefficients,~y Li and~y Ui,respectively.This task is realized for each selected membership loci of fuzzy datum,which become vertices of constructed convex hull.The possibility value(treated as a measure of goodness offit or a measure of compatibility between data and a regression mod-el),h=0.50,has been selected.The obtained values of the fuzzy parameters~a j are shown in Table4.We now employ the convex hull approach.As mentioned above, the selection process is based on the location of the data.Due to this selection procedure,we have found that the number of fuzzy data(points)is drastically reduced from12,800points to68points (P=68).In this manner we can carry out the implementation of LP for the convex hull without any substantial effort.Fig.6illustrates the possibilistic regression based on constructed convex hull polygon as well as vertices of the constructed convex hull(3-Dimension)being selected in this case.In addition,unselected points,which may have a potential to become convex vertices were scattered inside the constructed convex hull.Based on the example,it becomes apparent that the implemen-tation of convex hull based of IDA approach is efficient and may drastically reduce the complexity of the overall computing.Table 5offers some comparative insight into the performance of the IDA approach and the generic(ordinary)approach available in the literature.For comparative reasons,we show here a number of considered vertices used for the construction of the convex hull polygon.A reduced amount of selected points decreased the asso-ciated computational complexity.The reduction of time achieved in this selected case is96.6%. Table5includes a comparison of the computational time required to analyze OHSMS samples of data when running possibilistic regression with and without convex hull.Moreover,given the real-time environment data processing,it becomes apparent that the size of data set to be processed in-creases and this issue has to be handled in regression analysis and any subsequent implementation of the LPs.Additionally,other problems may arise when the related input variables were changed either receiving new influential factors or eliminating those se-lected factors.In this case the entire set of constraints must be reformulated.Needless to say that,under such circumstances, the computational complexity increases.Two major problems can be solved by implementing the selected IDA approach.As mentioned in the previous section,the analysis becomes simpler when determining the outside locus points,which initially represent as rectangle shape of membership function.These points were connected to each other to produce sufficient number of edges andfinally an optimum convex hull polygon will be con-structed efficiently.With the vertex points that are obtained from this constructed convex hull,the LP can be easily carried out to generate possibilistic regression,which was used to capture all data.Furthermore,the convex hull polygon built through using the selected points of loci may do not influence the obtained regression analysis results.Based on this theoretical point of view,we can stress that the implementation of possibilistic regression based on the convex hull approach becomes highly appropriate for analysis of the OHSMS influential factors.With respect to the fuzzy input/output data representation for these samples of data,we showed that selected IDA successfully perform an analysis process as well asTable3Samples of input and output data for200selected companies/organizations.Companies Inputs OutputOHSPP OHSCS OHSTS OHSHA OHSRC OHSPM OHSEIComp001(0.10,0.56,0.90)(0.70,0.83,0.88)(0.01,0.77,0.91)(0.31,0.43,0.57)(0.05,0.54,0.95)(0.13,0.38,0.66)(0.01,0.59,0.96) Comp002(0.58,0.62,0.89)(0.25,0.37,0.92)(0.08,0.33,0.78)(0.07,0.95,0.97)(0.19,0.82,0.86)(0.25,0.27,0.40)(0.10,0.87,0.40) Comp003(0.25,0.70,0.81)(0.36,0.46,0.72)(0.25,0.39,0.47)(0.02,0.41,0.48)(0.28,0.41,0.43)(0.03,0.26,0.97)(0.49,0.53,0.82) Comp004(0.24,0.74,0.84)(0.01,0.53,0.99)(0.08,0.53,0.87)(0.06,0.13,0.21)(0.04,0.11,0.20)(0.15,0.38,0.87)(0.52,0.71,0.82) Comp005(0.25,0.65,0.86)(0.11,0.30,0.46)(0.25,0.61,0.88)(0.15,0.25,0.53)(0.30,0.61,0.67)(0.31,0.35,0.41)(0.35,0.83,0.53)––––––––––––––––––––––––Comp196(0.07,0.34,0.54)(0.29,0.41,0.66)(0.07,0.46,0.84)(0.64,0.68,0.73)(0.44,0.46,0.76)(0.47,0.76,0.88)(0.06,0.24,0.79) Comp197(0.36,0.77,0.99)(0.38,0.66,0.78)(0.09,0.31,0.70)(0.47,0.64,0.88)(0.05,0.56,0.69)(0.27,0.42,0.45)(0.18,0.88,0.91) Comp198(0.04,0.18,0.98)(0.38,0.68,0.86)(0.02,0.65,0.71)(0.07,0.80,0.96)(0.33,0.59,0.68)(0.35,0.42,0.50)(0.38,0.68,0.79) Comp199(0.25,0.70,0.89)(0.35,0.74,0.79)(0.31,0.57,0.98)(0.06,0.41,0.82)(0.20,0.26,0.45)(0.05,0.30,0.37)(0.35,0.45,0.65) Comp200(0.41,0.55,0.89)(0.38,0.40,0.49)(0.32,0.33,0.51)(0.07,0.28,0.89)(0.05,0.10,0.12)(0.15,0.35,0.75)(0.18,0.25,0.71)Table4Values of the fuzzy parameters,~a jðh¼0:50Þ.Fuzzy parameter Center,m j Spread,c j~a0.650.47~a10.320.26~a2À0.520~a3À0.050~a40.140.09~a50.320.24~a 6À0.480A.A.Ramli et al./Safety Science49(2011)1110–11171115。
