考虑权重信息未知的区间直觉模糊三支群决策方法

本文提出优化视角下专家权重信息未知的区间直觉模糊三支群决策方法。首先利用区间直觉模糊加权平均算子集结不同专家提供的区间直觉模糊损失评价,获得群体综合损失评价结果。以专家个体与群体综合评价相似度越髙,越能反映群体综合评价意见且赋予髙的专家权重为原则,分别构建专家权重信息完全未知和部分已知的权重确定模型。进而建立确定区间直觉模糊三支决策概率阈值对的优化模型,并提出基于专家权重信息未知的区间直觉模糊三支群决策方法。最后,算例分析及比较结果表明所提出方法的有效性。     

Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis

Hesitant fuzzy sets (HFSs), which allow the membership degree of an element to a set represented by several possible values, can be considered as a powerful tool to express uncertain information in the process of group decision making. We derive some correlation coefficient formulas for HFSs and apply them to clustering analysis under hesitant fuzzy environments. Two real world examples, i.e. software evaluation and classification as well as the assessment of business failure risk, are employed to illustrate the actual need of the clustering algorithm based on HFSs, which can incorporate the difference of evaluation information provided by different experts in clustering processes. In order to extend the application domain of the clustering algorithm in the framework of HFSs, we develop the interval-valued HFSs and the corresponding correlation coefficient formulas, and then demonstrate their application in clustering with interval-valued hesitant fuzzy information through a specific numerical example.     

基于区间数决策矩阵的评判专家水平分析方法

在群决策分析中,如何评判专家水平是一个重要课题,针对群决策中基于区间数决策矩阵形式偏好信息的评判专家水平问题,提出了一种分析方法。首先,给出了有关区间数、专家群体区间数决策矩阵的定义及其决策矩阵的规范化方法;然后,通过定义专家与专家群体关于方案排序向量之间的偏差,给出了基于理想点法的区间数决策矩阵形式偏好信息的专家评判水平的分析方法。同时,利用聚类分析方法,给出了专家评判水平分类的判别方法;最后,通过一个算例说明给出的分析方法。     

Extension principles for interval-valued intuitionistic fuzzy sets and algebraic operations

The Atanassov’s intuitionistic fuzzy (IF) set theory has become a popular topic of investigation in the fuzzy set community. However, there is less investigation on the representation of level sets and extension principles for interval-valued intuitionistic fuzzy (IVIF) sets as well as algebraic operations. In this paper, firstly the representation theorem of IVIF sets is proposed by using the concept of level sets. Then, the extension principles of IVIF sets are developed based on the representation theorem. Finally, the addition, subtraction, multiplication and division operations over IVIF sets are defined based on the extension principle. The representation theorem and extension principles as well as algebraic operations form an important part of Atanassov’s IF set theory.     

A novel two-phase group decision making approach for construction project selection in a fuzzy environment

This paper considers a construction project problem under multiple criteria in a fuzzy environment and proposes a new two-phase group decision making (GDM) approach. This approach integrates a modified analytic network process (ANP) and an improved compromise ranking method, known as VIKOR. To take uncertainty and risk into account, a new decision making approach is presented with multiple fuzzy information by a group of experts, and a risk attitude for each expert is incorporated that can be expressed linguistically. First, a modified fuzzy ANP method is introduced to address the problem of dependence as well as feedback among conflicting criteria and to determine their relative importance. Then, a fuzzy VIKOR method is extended to rank potential projects on the basis of their overall performance. An illustrative example from the literature is provided for the construction project problem to demonstrate the effectiveness and feasibility of the proposed approach. The computational results show that the proposed two-phase GDM approach is suitable to cope with imprecision and subjectivity for the complicated decision making problem. Finally, the associated results of the proposed approach with risk attitudes and without risk attitudes are compared with the results reported by Cheng and Li [1], and the merits are highlighted.     

Group decision making based on novel fuzzy modified TOPSIS method

The aim of this paper is to present a novel fuzzy modified technique of order preference by a similarity to ideal solution (TOPSIS) method by a group of experts, which can select the best alternative by considering both conflicting quantitative and qualitative evaluation criteria in real-life applications. The proposed method satisfies the condition of being the closest to the fuzzy positive ideal solution and also being the farthest from the fuzzy negative ideal solution with multi-judges and multi-criteria. The performance rating values of alternatives versus conflicting criteria as well as the weights of criteria are described by linguistic variables and are transformed into triangular fuzzy numbers. Then a new collective index is introduced to discriminate among alternatives in the evaluation process with respect to subjective judgment and objective information. This paper shows that the proposed fuzzy modified TOPSIS method is a suitable decision making tool for the manufacturing decisions with two examples for the robot selection and rapid prototyping process selection.     

A financial alliance compromise between executives and supervisory authorities

In this paper, we are looking for the best financial alliance compromise structure between the executives of the banks and insurance companies and the bank and insurance supervisory authorities in Finland. First, we studied alternative alliance structures between banks and insurance companies from the point of view of supervisory authorities. Together with leaders and experts of the supervisory authorities, we introduced eight criteria for the evaluation of the six alternative alliance structures. The evaluation was carried out by an expert panel consisting of the representatives of the supervisory authorities.In our earlier research, the financial conglomerate was preferred by bank and insurance executives to the other alternatives. The alliance models based on plain cross-selling agreements received the highest ranks in the evaluation of supervisory authorities. Under certain conditions, the financial conglomerate might be an acceptable compromise alternative for the supervisory authorities as well.     

A method based on similarity measures for interactive group decision-making with intuitionistic fuzzy preference relations

In this paper, we study the group decision-making problem in which the preference information given by experts takes the form of intuitionistic fuzzy preference relations, and the information about experts’ weights is completely unknown. We first utilize the intuitionistic fuzzy weighted averaging operator to aggregate all individual intuitionistic fuzzy preference relations into a collective intuitionistic fuzzy preference relation. Then, based on the degree of similarity between the individual intuitionistic fuzzy preference relations and the collective one, we develop an approach to determine the experts’ weights. Furthermore, based on intuitionistic fuzzy preference relations, a practical interactive procedure for group decision-making is proposed, in which the similarity measures between the collective preference relation and intuitionistic fuzzy ideal solution are used to rank the given alternatives. Finally, an illustrative numerical example is given to verify the developed approach.     

模糊德尔菲层次分析法及其应用

将传统的层次分析法、模糊评价方法与群体决策的德尔菲方法有机地结合起来,给出了一种系统分析的新方法—模糊德尔菲层次分析法(FDAHP),该方法在群体的德尔菲调查的基础上,将群体对事物的两两判断进行模糊处理,并将群体整体判断的结果作为决策环境参数,进一步根据群体决策的乐观系数最终确定出群体对事物的综合权重.用一个简单例示说明了该方法的具体执行步骤及其可行性.最后对该方法的优缺点作了简要讨论,并提出了今后相关问题的可能研究课题.     

An approach to group decision making based on interval multiplicative and fuzzy preference relations by using projection

This paper presents a consensus model for group decision making with interval multiplicative and fuzzy preference relations based on two consensus criteria: (1) a consensus measure which indicates the agreement between experts’ preference relations and (2) a measure of proximity to find out how far the individual opinions are from the group opinion. These measures are calculated by using the relative projections of individual preference relations on the collective one, which are obtained by extending the relative projection of vectors. First, the weights of experts are determined by the relative projections of individual preference relations on the initial collective one. Then using the weights of experts, all individual preference relations are aggregated into a collective one. The consensus and proximity measures are calculated by using the relative projections of experts’ preference relations respectively. The consensus measure is used to guide the consensus process until the collective solution is achieved. The proximity measure is used to guide the discussion phase of consensus reaching process. In such a way, an iterative algorithm is designed to guide the experts in the consensus reaching process. Finally the expected value preference relations are defined to transform the interval collective preference relation to a crisp one and the weights of alternatives are obtained from the expected value preference relations. Two numerical examples are given to illustrate the models and approaches.     

Comparison of first aggregation and last aggregation in fuzzy group TOPSIS

The Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS), one of the major multi attribute decision making (MADM) techniques, ranks the alternatives according to their distances from the ideal and the negative ideal solution. In real evaluation and decision making problems, it is vital to involve several people and experts from different functional areas in decision making process. Also under many conditions, crisp data are inadequate to model real-life situations, since human judgments including preferences are often vague and cannot estimate his preference with an exact numerical value. Therefore aggregation of fuzzy concept, group decision making and TOPSIS methods that we denote “fuzzy group TOPSIS” is more practical than original TOPSIS.     

基于局部评价环境的群组评价状态测评研究

群组评价状态测评是提高群组评价方法适用性和有效性的途径之一,以评价参与者为节点,构建具有评价群体之间链接关系的群体网络结构,即评价局部环境,将评价群体网络结构信息与属性信息进行整合构造局部评价环境的群组评价状态测度,实现协商过程有效跟随,实时对评价参与者和群组评价状态进行测评。根据测评结果给出具有评价参与者核心性测度、群体协商充分性和有效性测度的建议,对评价参与者的评价行为进行引导,给出具有导向性的评价信息集结方法建议。给出示例对群组评价状态测评进行示范解释。     

A complex multi-attribute large-group PLS decision-making method in the interval-valued intuitionistic fuzzy environment

In the complex multi-attribute large-group decision-making (CMALGDM) problems in interval-valued intuitionistic fuzzy (IVIF) environment, attributes of the alternatives are often stratified and correlated. This paper proposes a decision-making method for these problems based on partial least squares (PLS) path modelling, which not only fully exploits the decision information of decision makers (DMs), but also effectively addresses the relativity problem in the decision attributes and objectively assigned weights to the primary decision attributes (i.e., “latent variables for decision making”). The method can be outlined in three steps. First, a two-stage method is proposed to transform the interval-valued intuitionistic fuzzy number (IVIFN) samples into single-valued samples. In this step, an improved C-OWA operator is first given to transform the IVIFN samples into intuitionistic fuzzy number (IFN) samples, which makes the preference information of the DMs more objectively aggregated. Then a proposed membership-based method is applied to reduce the information loss and transform the IFN samples into single-valued samples. Second, the estimated values and weights of the “latent variables for decision-making” are obtained by means of the PLS path modelling algorithm. Finally, a multi-alternative sorting method is devised in accordance with the estimated values and weights. An example is provided to illustrate the proposed technique and evaluate its feasibility and validity.     

基于参数设计的信噪比交叉效率评价方法

针对DEA交叉效率评价过程中没有考虑自评与互评效率的作用而主观赋予相同权重导致交叉效率评价值不准确的问题.文章基于参数设计的思想,依据试验设计中可控与不可控因素的作用机理区分自评权重和互评权重对所评价决策单元交叉效率的影响与作用,将其界定为可控与不可控因素的管理学属性,明确不同权重作用机理;引入信噪比作为衡量决策单元交叉效率评价时的性能指标,实施DEA交叉效率评价方法的改进,设计出DEA信噪比交叉效率集结方法,从而实现交叉效率的集结方式由单一考虑交叉效率波动的均值转化为综合考虑交叉效率波动情况(均值与方差),交叉效率评价值用信噪比交叉效率替代交叉效率平均值更具有统计学意义并可从管理学角度解释,评价结果也具有更高的可区分性;最后通过算例分析验证了交叉效率评价理论上的必要性和该方法的合理性与可行性,同时发现了交叉效率评价中存在CCR有效DMU序位超出了有效DMU范围现象,建议应实施同质DMU检验和评价值归一化.文章的研究也为提高DEA交叉效率测算的准确性提供一种新思路.     

Determining an optimum location for an undesirable facility in a workroom environment

This paper deals with the problem of placing an undesirable but necessary piece of equipment, process or facility into a working environment. Locating a piece of equipment that produces contaminants or creates stresses for nearby workers, placing a storage facility for flammable materials or locating hazardous waste in the workroom environment, are all typical examples of the undesirable facility location problem. The degree of undesirability between an existing facility or worker and the new undesirable entity is reflected through a weighting factor. The problem is formally defined to be the selection of a location within the convex region that maximizes the minimum weighted Euclidean distance with respect to all existing facilities. A ‘Maximin’ model is formulated and two solution procedures introduced. A geometrical approach and an algorithmic approach are described in detail. An example is provided for each solution procedure and the computational efficiency of the algorithm is discussed and illustrated.     

The assessment of the information quality with the aid of multiple criteria analysis

The virtual business work flow depends on the information quality (IQ) which is essential attribute of information. The IQ depends strongly on organization of the information system (IS) and how the information is processed. In our approach we incorporate the four-aspect representation of IQ: (1) intrinsic, (2) contextual, (3) representational, and (4) accessibility. These four-aspects are divided into several criteria at the next level of hierarchy. The weights, representing the relative importance of criteria, have been assessed by pair-wise comparisons made by group of experts. Based on discussion with experts, six alternative strategies, that could be used for improving the IQ, were designed. For each given criterion, the group of subjects revealed the opinion about the level of achievement of every alternative. The set of scores, assigned to the alternative by different subjects, formed the discrete distribution that is used for a comparison of alternatives with the aid of stochastic dominances. In analogy to the Electre I methodology, the simple algorithm for the aggregate evaluation of analyzed alternatives was proposed. The benefits of proposed approach were demonstrated in a case study of the semiconductor industry. The results of our study suggest, that in case of matured company, the external strategies, that point out to the information exchange and strategic networked alliance with customers and suppliers, are preferred to the internal ones. The latter ones might be of greater importance for the new set up or for a young company.     

基于二维二元语义和模糊AHP-TODIM的低碳供应商选择方法

针对专家给出二维语言评价信息的低碳供应商评选问题,提出一种基于二维二元语义和模糊AHP-TODIM的方法。该方法首先提出改进的二元语义模型,基于此定义二维二元语义及其加权平均算子。接着构建低碳供应商评价的指标体系。最后,将专家给出的二维语言评价信息转化为二维二元语义,使用模糊AHP法计算指标权重,并利用二维二元语义加权平均算子集结信息,在此基础上将TODIM方法扩展到二维二元语义环境以获取低碳供应商排序。案例分析说明了所提出的方法的有效性。     

基于前景理论与PROMETHEE的FMEA风险评估

针对考虑群体评价一致性和专家心理感知行为影响的失效模式及影响分析风险评估问题,提出了基于前景理论和偏好序结构排序法(PROMETHEE)的风险评估方法。首先,专家团队采用语言变量表征风险因子评价信息,利用直觉模糊熵确定风险因子客观权重;其次,采用灰关联度刻画专家评价与群体评价的一致性,以最大化关联度和极大熵准则构建专家权重优化模型;然后,集成风险因子和专家的主客观权重,获得风险因子及专家的综合权重;再次,运用直觉模糊加权平均算子集结专家评价信息,进而借助前景理论构建反应专家心理感知的前景矩阵;最后,基于PROMETHEE方法确定失效模式风险排序,并利用液晶显示器的案例验证了所提方法的有效性和可行性。     

Approach to group decision making based on determining the weights of experts by using projection method

The aim of this paper is to present a new approach for determining weights of experts in the group decision making problems. Group decision making has become a very active research field over the last decade. Especially, the investigation to determine weights of experts for group decision making has attracted great interests from researchers recently and some approaches have been developed. In this paper, the weights of experts are determined in the group decision environment via projection method. First of all, the average decision of all individual decisions is defined as the ideal decision. After that, the weight of expert is determined by the projection of individual decision on the ideal decision. By using the weights of experts, all individual decisions are aggregate into a collective decision. Then an ideal solution of alternatives of the collective decision, expressed by a vector, is determined. Further, the preference order of alternatives are ranked in accordance with the projections of alternatives on the ideal solution. Comparisons with an extended TOPSIS method are also made. Finally, an example is provided to illustrate the developed approach.     

基于层次分析法的毕业论文(设计)综合评价方法

毕业论文是高校实施教学计划的重要环节.针对目前很多高校毕业论文评价方法中存在的一些问题,结合论文评价过程的相关特点,在层次分析法(AHP)的基础上提出了群组AHP模型和模糊AHP模型两种决策优化模型,给出了基于这两种模型的高校学生毕业论文综合评价方法.实践表明,在对学生论文进行评价的过程中,方法具有合理、公正、简便、灵活、易于推广的特点,开发的基于该方法的毕业论文评价系统具有很强的应用价值.