基于犹豫模糊语言多属性群决策的VIKOR扩展方法

针对犹豫模糊语言多属性群决策问题,提出了一种基于可能度分布的VIKOR方法。该方法首先将基于犹豫模糊语言的评价信息转化成可能度分布值,定义了新的距离公式,避免了传统犹豫模糊语言评价信息在计算过程中造成的信息扭曲。然后,设计了基于最大群体效用与最小个体遗憾两个目标的群体信息集结优化模型,并给出多属性群决策的VIKOR扩展方法。运用一个交通建设方案选择的案例分析验证了方法的有效性和优越性。     

犹豫模糊语言群决策的共识性模型

针对犹豫模糊语言群决策问题,研究其共识性调整方法.首先,定义犹豫模糊语言术语集的距离测度;然后,基于该距离测度定义犹豫模糊决策矩阵间的共识性水平及其相关概念,建立共识性调整模型,该模型采用反馈机制,并且尽可能提供给专家较多的信息,以方便专家进行信息修正,达到群体共识;最后,通过具体实例说明了所提出的共识性方法的可行性和实用性.     

Clustering-based method for large group decision making with hesitant fuzzy linguistic information: Integrating correlation and consensus

Aiming at the large-scale experts and the lower consensus in large group decision making, a novel clustering-based method integrating correlation and consensus of hesitant fuzzy linguistic information is proposed. Firstly, develop a new hesitant degree function for hesitant fuzzy linguistic element considering its scale. Secondly, put forward the correlation measure and consensus measure models combining the hesitant degree. And then present a clustering method integrating the correlation and consensus to divide the large-scale experts into several clusters. The clustering method simultaneously ensures the cohesion of clusters and the gradual increasing of the collective consensus level. After clustering, activate the selection process to update the weights of clusters combining the number of experts in clusters and the consensus level of clusters and use the score function considering the hesitant degree to rank the alternatives. Finally, a case and some comparisons are studied and analyzed to verify the rationality and effectiveness of the method.     

面向犹豫模糊语言信息的大型群体分类集结模型

研究基于犹豫模糊语言信息的大型群体决策分类和集结问题.提出一种面向犹豫模糊语言信息的专家相似度构建方法,相似度测算基于犹豫相似度和距离相似度综合考虑;改进编网分类方法,借助基于相似矩阵的编网分类方法对大型群体专家进行初步分类,确定可接受范围,对专家进行再分类并通过分类精度指标对分类的有效性进行验证以确定最终类别;构建大规模群体信息集结的类内集结和类间集结框架,对类内专家信息进行集结以获得概率语言信息;提出一种基于语言概率分布的类可靠度计算方法,基于类可靠度和类专家数量占总体数量比例综合考虑确定类别权重以实现类间信息集结,进而根据集结的概率语言信息计算对象期望值并进行排序.最后,通过算例及方法比较验证所提出方法的有效性.     

三角模糊数型多准则群决策的VIKOR扩展方法

运用VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR)方法研究模糊多准则群决策问题常常将其分成模糊信息集结和VIKOR方法求解两个阶段。个体评估信息集结方法不同,所得到的群体集结结果也不同,获得的妥协解可能会存在较大差异。鉴于此,基于含有三角模糊数的多准则群决策问题,分析现有两种主流群体信息集结方法存在的缺陷,基于个体评估值与群体评估值的距离最优和较高的相似度两个目标,设计群体信息集结优化模型,提出一种拓展的VIKOR方法。最后通过实例分析说明了所提出方法的有效性和可行性。     

Consensus-reaching methods for hesitant fuzzy multiple criteria group decision making with hesitant fuzzy decision making matrices

Group decision making plays an important role in various fields of management decision and economics. In this paper, we develop two methods for hesitant fuzzy multiple criteria group decision making with group consensus in which all the experts use hesitant fuzzy decision matrices (HFDMs) to express their preferences. The aim of this paper is to present two novel consensus models applied in different group decision making situations, which are composed of consensus checking processes, consensus-reaching processes, and selection processes. All the experts make their own judgments on each alternative over multiple criteria by hesitant fuzzy sets, and then the aggregation of each hesitant fuzzy set under each criterion is calculated by the aggregation operators. Furthermore, we can calculate the distance between any two aggregations of hesitant fuzzy sets, based on which the deviation between any two experts is yielded. After introducing the consensus measure, we develop two kinds of consensus-reaching procedures and then propose two step-by-step algorithms for hesitant fuzzy multiple criteria group decision making. A numerical example concerning the selection of selling ways about ‘Trade-Ins’ for Apple Inc. is provided to illustrate and verify the developed approaches. In this example, the methods which aim to reach a high consensus of all the experts before the selection process can avoid some experts’ preference values being too high or too low. After modifying the previous preference information by using our consensus measures, the result of the selection process is much more reasonable.     

基于Pythagorean不确定语言的扩展VIKOR多属性群决策方法

针对属性值为Pythagorean不确定语言变量,属性权重和专家权重完全未知的群决策问题,提出一种扩展VIKOR多属性群决策方法.首先,给出Pythagorean不确定语言变量的概念,提出考虑语义变化的Pythagorean不确定语言变量运算规则、大小比较方法和Hamming距离测度;其次,提出基于Pythagorean 不确定语言模糊熵的属性权重确定方法和基于相似度的专家权重确定方法,进而提出一种新的扩展VIKOR方法;最后,通过国内航空公司服务质量评估实例验证所提出方法的有效性和可行性.     

A group decision making framework based on fuzzy VIKOR approach for machine tool selection with linguistic information

Computer numerical control (CNC) machines are used for repetitive, difficult and unsafe manufacturing tasks that require a high degree of accuracy. However, when selecting an appropriate CNC machine, multiple criteria need to be considered by multiple decision makers. In this study, a multi-criteria group decision making (MCGDM) technique based on the fuzzy VIKOR method is developed to solve a CNC machine tool selection problem. Linguistic variables represented by triangular fuzzy numbers are used to reflect decision maker preferences for the criteria importance weights and the performance ratings. After the individual preferences are aggregated or after the separation values are computed, they are then defuzzified. In this paper, two algorithms based on a fuzzy linguistic approach are developed. Based on these two algorithms and the VIKOR method, a general MCGDM framework is proposed. A CNC machine tool selection example illustrates the application of the proposed approach. A comparative study of the two algorithms using the above case study information highlighted the need to combine the ranking results, as both algorithms have distinct characteristics.     

A novel hesitant fuzzy linguistic hybrid cloud model and extended best-worst method for multicriteria decision making

Developing effective and accurate model to handle complex uncertainties of linguistic assessments in multicriteria decision making (MCDM) has important theoretical significance and practical value of engineering. This paper proposes a novel hesitant fuzzy linguistic hybrid cloud (HFLHC) model that integrates hesitant fuzzy linguistic term set and cloud model to handle the hesitancy, fuzziness, and randomness of linguistic expression. The normal cloud and trapezium cloud are integrated to represent hybrid-length linguistic variables of HFLHC model, which can effectively avoid evaluation information loss and distortion. Aiming at applying HFLHC model to MCDM, some hybrid operations for normal cloud and trapezium cloud are developed. Moreover, an improved method for aggregating multiple linguistic concepts into an integrated trapezium cloud in HFLHC model is proposed, with consideration of the different representation region of each linguistic concept. Furthermore, a novel HFLHC-based best-worst method is proposed to obtain optimal criteria weights with developing a HFLHC optimization programming model and a modified consistency ratio. Finally, an illustrative example of sustainable supplier selection is presented. Several comparative analyses demonstrate that our method can provide more consistency and greater reliability.     

模糊语言多属性群决策的客观综合赋权方法

针对一类属性及专家权重完全未知且评价值为直觉不确定语言数的多属性群决策问题,提出一种基于客观综合赋权模型的模糊群决策方法。通过定义直觉不确定语言数的不确定度和距离测度,对单个专家内部以及专家群体之间的评价值进行分析,分别建立基于离差最大化和熵值的属性综合赋权模型以及基于不确定度和偏离度的专家综合赋权模型,提出一种基于客观综合权重的直觉不确定语言多属性群决策方法。通过实例分析表明了该方法的可行性和实用性。     

基于动态P-模糊语言算子的VIKOR决策方法

针对直觉模糊信息解决动态多属性决策问题时存在的不足,将Pythagorean模糊语言信息引入到动态多属性决策问题,提出一种基于Pythagorean模糊语言信息集成算子的多准则妥协排序（VIKOR）决策方法。引入Pythagorean模糊语言得分函数、精确函数、距离计算公式等概念,提出动态 Pythagorean模糊语言加权平均（DPFLWA）算子,并研究DPFLWA算子的基本性质。最后,基于DPFLWA算子和VIKOR方法,构建一种动态 Pythagorean模糊语言多属性决策方法。通过第三方逆向物流服务商的选择实例,表明该方法的可行性和有效性。     

A method for group decision making with multi-granularity linguistic assessment information

This paper proposes a method to solve the group decision making (GDM) problems with multi-granularity linguistic assessment information. In the method, the multi-granularity linguistic information provided by experts is firstly expressed in the form of fuzzy numbers. In order to make the collective opinion close to each expert’s opinion, a linear goal programming model is constructed to integrate the fuzzy assessment information and to directly compute the collective ranking values of alternatives without the need of information transformation. Then, a fuzzy preference relation on the pairwise comparisons of the collective ranking values of alternatives is constructed using the dominance possibility degree of the comparison between the fuzzy numbers. By applying a non-dominance choice degree to this fuzzy preference relation, the ranking of alternatives is determined and the most desirable alternative(s) is selected. An example is used to illustrate the applicability of the proposed method and its advantages.     

An extended COPRAS method for multiattribute group decision making based on dual hesitant fuzzy Maclaurin symmetric mean

The well-known Maclaurin symmetric mean (MSM) and the dual MSM (DMSM) are introduced as important operators to handle multiattribute group decision making (MAGDM) information. The MSM and the DMSM operators have the prominent characteristic of accurately describing the interdependence of multi-input arguments. Due to their advantage, we extend the MSM and the DMSM into the dual hesitant fuzzy environment to aggregate uncertain information. Particularly, we propose some novel aggregation operators, namely dual hesitant fuzzy MSM, weighted dual hesitant fuzzy MSM, dual hesitant fuzzy dual MSM, and weighted dual hesitant fuzzy dual MSM operators. Moreover, we study some properties and special remarks regarding different values of the parameter. With an extension of the complex proportional assessment method, we formulate a new approach for the dual hesitant fuzzy MAGDM. Finally, we test the applicability and feasibility of our proposed method by solving a mobile payment platform selection problem in Ghana.     

广义犹豫模糊信息集成及其多属性群决策

在犹豫模糊环境下,主要研究了基于阿基米德范数的广义信息集成算法,并提出了一种新的多属性群决策方法。基于阿基米德T-范数和S-范数,定义了广义犹豫模糊运算法则;运用新定义的广义犹豫模糊运算法则,提出了广义犹豫模糊有序加权平均(G-HFOWA)算子,研究了其优良性质;探讨了在某些特殊情况下,广义犹豫模糊有序加权平均算子将转化为一些常见的犹豫模糊信息集成算子,包括犹豫模糊有序加权平均算子、犹豫模糊Einstein有序加权平均算子、犹豫模糊Hamacher有序加权平均算子以及犹豫模糊Frank有序加权平均算子;基于广义信息集成算子,构建了一种新的犹豫模糊多属性群决策方法,并将其应用于区域经济协调发展研究过程中,以验证提出的决策方法是可行的与有效的。     

Extension of the VIKOR method to dynamic intuitionistic fuzzy multiple attribute decision making

In this paper, we extend the VIKOR method for dynamic intuitionistic fuzzy multiple attribute decision making (DIF-MADM). Two new aggregation operators called dynamic intuitionistic fuzzy weighted geometric (DIFWG) operator and uncertain dynamic intuitionistic fuzzy weighted geometric (UDIFWG) operator are presented. Based on the DIFWA and UDIFWA operators respectively, we develop two procedures to solve the DIF-MADM problems where all attribute values are expressed in intuitionistic fuzzy numbers or interval-valued intuitionistic fuzzy numbers, which are collected at different periods. Finally, a numerical example is used to illustrate the applicability of the proposed approach.     

Extension of TOPSIS method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information

With respect to linguistic multiple attribute group decision making problems with incomplete weight information, a new method is proposed. In the method, the 2-tuple linguistic representation developed in recent years is used to aggregate the linguistic assessment information. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional technique for order performance by similarity to ideal solution, by which the attribute weights can be determined. Then, the optimal alternative(s) is determined by calculating the shortest distance from the 2-tuple linguistic positive ideal solution, and on the other side, the farthest distance of the 2-tuple linguistic negative ideal solution. The method has exact characteristic in linguistic information processing. It avoided information distortion and losing, which occur formerly in the linguistic information processing. Finally, a numerical example is used to illustrate the use of the proposed method. The result shows the approach is simple, effective, and easy to calculate.     

区间模糊语言多属性群决策方法及应用研究

基于我国银行业所面临的数据匮乏、信息披露制度不完善等问题,国际上先进的统计量化方法并不能完全适用于对我国操作风险的评价,从定性和定量相结合的角度出发,针对操作风险评价中的多属性群决策问题,提出一种在区间模糊语言信息下基于不确定的拓展有序加权平均算子（UEOWA）和不确定语言混合集结算子（ULHA）的多专家多属性商业银行操作风险评价方法,构建基于区间模糊语言的评价集来描述专家不精确、难量化的意见,梳理评价思路,设计评价步骤,通过实例验证了该方法的可操作性和有效性。     

基于MACBETH方法的犹豫模糊语言多准则决策方法

犹豫模糊语言集是语言术语集的拓展.受传统的MACBETH(measuring attractiveness by a categorical-based evaluation technique)方法的启发,构建基于MACBETH方法的犹豫模糊语言多准则决策方法.首先将语言表达式表示的决策信息通过转化函数转化为犹豫模糊语言数,进而得出犹豫模糊语言判断矩阵;然后将此结果应用于改进的MACBETH决策支持系统;最后,通过毕业生选择就职企业这一实例说明该方法的有效性和可行性.     

Multi-criteria group decision making with incomplete hesitant fuzzy preference relations

In order to simulate the hesitancy and uncertainty associated with impression or vagueness, a decision maker may give her/his judgments by means of hesitant fuzzy preference relations in the process of decision making. The study of their consistency becomes a very important aspect to avoid a misleading solution. This paper defines the concept of additive consistent hesitant fuzzy preference relations. The characterizations of additive consistent hesitant fuzzy preference relations are studied in detail. Owing to the limitations of the experts’ professional knowledge and experience, the provided preferences in a hesitant fuzzy preference relation are usually incomplete. Consequently, this paper introduces the concepts of incomplete hesitant fuzzy preference relation, acceptable incomplete hesitant fuzzy preference relation, and additive consistent incomplete hesitant fuzzy preference relation. Then, two estimation procedures are developed to estimate the missing information in an expert's incomplete hesitant fuzzy preference relation. The first procedure is used to construct an additive consistent hesitant fuzzy preference relation from the lowest possible number, (n − 1), of pairwise comparisons. The second one is designed for the estimation of missing elements of the acceptable incomplete hesitant fuzzy preference relations with more known judgments. Moreover, an algorithm is given to solve the multi-criteria group decision making problem with incomplete hesitant fuzzy preference relations. Finally, a numerical example is provided to illustrate the solution processes of the developed algorithm and to verify its effectiveness and practicality.     

Interval programming method for hesitant fuzzy multi-attribute group decision making with incomplete preference over alternatives

The aim of this study is to employ the main structure of LINMAP (LINear programming technique for Multidimensional Analysis of Preference) to propose an interval programming method for solving multi-attribute group decision making (MAGDM) problems in which the ratings of alternatives are taken as hesitant fuzzy elements (HFEs) and all pair-wise comparison judgments over alternatives are represented by interval numbers. The contribution of this study is fivefold: (1) we define the new consistency and inconsistency indices; (2) we construct an interval programming model to determine the hesitant fuzzy positive ideal solution and the optimal weights of attributes, and at the same time present a decision algorithm; (3) we discuss several special cases of the proposed model in detail; (4) we show that compared with intuitionistic fuzzy LINMAP method (Li et al., 2010), the proposed approach reveals more useful information including the interval preference information, and does not need to transform HFEs into intuitionistic fuzzy numbers but directly deals with MAGDM problems and thus obtains better final decision results; and (5) we demonstrate the applicability and implementation process of the proposed approach by using an energy project selection example.