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.     

An approach to group decision making with heterogeneous incomplete uncertain preference relations

For practical group decision making problems, decision makers tend to provide heterogeneous uncertain preference relations due to the uncertainty of the decision environment and the difference of cultures and education backgrounds. Sometimes, decision makers may not have an in-depth knowledge of the problem to be solved and provide incomplete preference relations. In this paper, we focus on group decision making (GDM) problems with heterogeneous incomplete uncertain preference relations, including uncertain multiplicative preference relations, uncertain fuzzy preference relations, uncertain linguistic preference relations and intuitionistic fuzzy preference relations. To deal with such GDM problems, a decision analysis method is proposed. Based on the multiplicative consistency of uncertain preference relations, a bi-objective optimization model which aims to maximize both the group consensus and the individual consistency of each decision maker is established. By solving the optimization model, the priority weights of alternatives can be obtained. Finally, some illustrative examples are used to show the feasibility and effectiveness of the proposed method.     

A consensus model for group decision making under trapezoidal fuzzy numbers environment

Natural linguistic terms can preferably express the opinions of decision makers in complicated decision environment. Group decision making with multiplicative trapezoidal fuzzy preference relations transforming from natural linguistic terms attracts the attention of researchers for its important research significant. The developed approach is based on consensus improving process by using a new similarity measure and a trapezoidal fuzzy power ordered weighted geometric averaging (TFPOWGA) operator. In order to introduce this approach, firstly, trapezoidal fuzzy power geometric averaging operator and TFPOWGA operator are presented to aggregate trapezoidal fuzzy numbers (TFNs). Secondly, a new similarity measure for TFNs is introduced by combining centroids and areas of TFNs. We further propose a new consensus improving algorithm that consists of consensus measure and a dynamic feedback mechanism containing a multi-objective optimization model and some indirect rules. And then a selection stage is described to rank the alternatives. At last, an example is implemented to demonstrate effectiveness of the approach.

     

Some interesting properties of the fuzzy linguistic model based on discrete fuzzy numbers to manage hesitant fuzzy linguistic information

The management of hesitant fuzzy information is a topic of special interest in fuzzy decision making. In this paper, we focus on the use and properties of the fuzzy linguistic modelling based on discrete fuzzy numbers to manage hesitant fuzzy linguistic information. Among these properties, we can highlight the existence of aggregation functions with no need of transformations or the possibility of a greater flexibilization of the opinions of the experts, even using different linguistic chains (multigranularity). Furthermore, based on these properties we perform a comparison between this model and the one based on hesitant fuzzy linguistic term sets, showing the advantages of the former with respect to the latter. Finally, a fuzzy decision making model based on discrete fuzzy numbers is proposed.     

Adaptive consensus model with multiplicative linguistic preferences based on fuzzy information granulation

An adaptive consensus model based on fuzzy information granulation (fuzzy IG) is presented for group consensus decision-making problems with multiplicative linguistic preference relations (MLPRs). Firstly, a granular representation of linguistic terms is concerned with the triangular fuzzy formation of a family of information granules over given Analytical Hierarchy Process (AHP) numerical scales. On this basis, the individual consistency and group consensus measure indices using fuzzy granulation technique are constructed, respectively. Then, the optimal cut-off points of fuzzy information granules are obtained by establishing a multi-objective optimization model together with a multi-objective particle swarm optimization (MOPSO) algorithm. A novel group consensus decision-making approach where consensus reaching process (CRP) is achieved by adaptively adjusting individual preferences through the optimization of the cut-off points is proposed. After conflict elimination, the obtained group preference gives the ranking of the alternatives. Finally, a real emergency decision-making case for liquid ammonia leak is given to illustrate the application steps of the proposed method and comparative analysis with the existing GDM methods. Comparative results demonstrate that the proposed method has some advantages in aspects of avoiding information loss or distortion and improving consensus performance.     

Consensus under a fuzzy context: Taxonomy,analysis framework AFRYCA and experimental case of study

Consensus reaching processes play an increasingly important role in the resolution of group decision making problems: a solution acceptable to all the experts participating in a problem is necessary in many real-life contexts. A large number of consensus approaches have been proposed to support groups in such processes, each one with its own characteristics, such as the methods utilized for the fusion of information regarding the preferences of experts. Given this variety of existing approaches in the literature to support consensus reaching processes, this paper considers two main objectives. Firstly, we propose a taxonomy that provides an overview and categorization of some existing consensus models for group decision making problems defined in a fuzzy context, taking into account the main features of each model. Secondly, the paper presents AFRYCA, a simulation-based analysis framework for the resolution of group decision making problems by means of different consensus models. The framework is aimed at facilitating a study of the performance of each consensus model, as well as determining the most suitable model/s for the resolution of a specific problem. An experimental study is carried out to show the usefulness of the framework.     

Ranking fuzzy numbers with an area method using radius of gyration

Ranking fuzzy numbers plays an very important role in linguistic decision making and some other fuzzy application systems. Many methods have been proposed to deal with ranking fuzzy numbers. Chu pointed out some shortcomings of the existing distance method and proposed to rank the fuzzy numbers with the area between the centroid point and original point. However, drawbacks are also found in the area method. For example, it cannot rank fuzzy numbers when some fuzzy numbers have the same centroid point. In this paper, we propose a modified area method to rank fuzzy numbers. The modified method can effectively rank various fuzzy numbers and their images. We also used some comparative examples to illustrate the advantage of the proposed method.     

基于语言共识模型的电子商务信用风险评价方法

电子商务信用风险评价能够更好地维护市场规则并防范交易主体的合法权益.从语言评价信息的角度,利用多属性群决策方法对电子商务信用风险评价方法进行探讨.首先,提出个体语言共识测度和群体语言共识测度;然后,针对共识性水平较低的决策群体,构建一种整数规划模型,用于调整决策者给出的初始语言决策信息;最后,提出一种基于语言共识模型的电子商务信用风险评价方法,并通过电子商务信用风险评价问题说明该方法的可行性和有效性.     

An adaptive consensus method for multi-attribute group decision making under uncertain linguistic environment

For a multi-attribute group decision making (MAGDM) problem, the so-called consensus reaching process is used to achieve an agreement among experts and finally make a common decision. Unfortunately, so far the consensus models for MAGDM haven’t been completely studied, especially for MAGDM under uncertain linguistic environment. The disadvantages of most existing consensus models could be summarized into 3 aspects. (1) In most existing consensus models, all the experts’ opinions are weighted equally important, and/or all the experts’ weights are treated statically. (2) Most of the interactive consensus methods are lack of effective feedback mechanism, while the automatic ones also have some defects, such as the lack of pertinence in adjustment process and the inability to reflect the subjective opinions of experts. (3) Also the comparison methods for uncertain linguistic variables therein are far from perfect, which require either complicated computing process or may cause non-distinguishable cases. In order to solve the above problems and obtain final decision results more efficiently, an interactive method with adaptive experts’ weights and explicit guidance rules for MAGDM under uncertain linguistic environment is developed. Our contributions can be summarized as follows. (1) Based on the definitions of closeness and consensus indices, a non-linear programming model is constructed to dynamically adjust the experts’ weights by maximizing the group consensus. (2) A targeted feedback mechanism including identification rules and recommendation rules is designed to guide the experts to modify their opinions more precisely and effectively. (3) A more appropriate method for comparing uncertain linguistic variables named dominance index is proposed, which can simplify the calculation process significantly. Finally, an illustrative example proves that the proposed consensus method is feasible and effective, and a detailed comparison and analysis highlights the advantages and characteristics of this method.     

A Novel Approach for Linguistic Group Decision Making Based on Generalized Interval‐Valued Intuitionistic Fuzzy Linguistic Induced Hybrid Operator and TOPSIS

In the multiple attribute linguistic group decision making analysis with interval‐valued intuitionistic fuzzy linguistic information, seeking highly efficient aggregation method and order relation play a crucial role. In this paper, we redefine an interval‐valued intuitionistic fuzzy linguistic variable that considers principal component and propose generalized interval‐valued intuitionistic fuzzy linguistic induced hybrid aggregation (GIVIFLIHA) operator with entropic order‐inducing variable and interval‐valued intuitionistic fuzzy linguistic technique for order preference by similarity to an ideal solution (TOPSIS) order relation based on interval‐valued intuitionistic fuzzy linguistic distance measure. Then, some primary properties of the GIVIFLIHA operator are discussed, and a linguistic group decision‐making approach based on GIVIFLIHA operator and interval‐valued intuitionistic fuzzy linguistic TOPSIS order relation is proposed. Finally, a numerical example concerning the investment strategy is given to illustrate the validity and applicability of the proposed method, and then the method is compared with the existing method to further illustrate its flexibility.     

A consensus model for group decision making problems with linguistic interval fuzzy preference relations

Sometimes, we find decision situations in which it is difficult to express some preferences by means of concrete preference degrees. In this paper, we present a consensus model for group decision making problems in which the experts use linguistic interval fuzzy preference relations to represent their preferences. This model is based on two consensus criteria, a consensus measure and a proximity measure, and on the concept of coincidence among preferences. We compute both consensus criteria in the three representation levels of a preference relation and design an automatic feedback mechanism to guide experts in the consensus reaching process.     

Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision‐making process

In this article, a new linguistic Pythagorean fuzzy set (LPFS) is presented by combining the concepts of a Pythagorean fuzzy set and linguistic fuzzy set. LPFS is a better way to deal with the uncertain and imprecise information in decision making, which is characterized by linguistic membership and nonmembership degrees. Some of the basic operational laws, score, and accuracy functions are defined to compare the two or more linguistic Pythagorean fuzzy numbers and their properties are investigated in detail. Based on the norm operations, some series of the linguistic Pythagorean weighted averaging and geometric aggregation operators, named as linguistic Pythagorean fuzzy weighted average and geometric, ordered weighted average and geometric with linguistic Pythagorean fuzzy information are proposed. Furthermore, a multiattribute decision‐making method is established based on these operators. Finally, an illustrative example is used to illustrate the applicability and validity of the proposed approach and compare the results with the existing methods to show the effectiveness of it.     

基于勾股模糊语言幂加权平均算子的多属性群体决策方法

针对多属性群决策问题,采用能够方便专家参考语言集信息进行评价并且取值灵活的勾股模糊语言集进行了处理。首先,基于语言集和勾股模糊集的距离测度给出了勾股模糊语言数距离测度的定义与相关性质;然后,以勾股模糊语言数的距离测度作为幂均（PA）算子的距离度量,提出了勾股模糊语言幂加权平均（PFLPWA）算子用以对群决策过程中不同专家评价矩阵进行融合,并同时在融合过程中考虑专家评价的差异性;最后,基于PFLPWA算子构建了勾股模糊语言环境下的群体决策新方法,并通过案例分析检验了PFLPWA算子应用于群决策中的有效性和适用性。     

Aggregating decision information into Atanassov's intuitionistic fuzzy numbers for heterogeneous multi-attribute group decision making

The aim of this paper is to propose a new aggregation method to solve heterogeneous MAGDM problem which involves real numbers, interval numbers, triangular fuzzy numbers (TFNs), trapezoidal fuzzy numbers (TrFNs), linguistic values and Atanassov's intuitionistic fuzzy numbers (AIFNs). Firstly, motivated by the relative closeness of technique for order preference by similarity to ideal solution (TOPSIS), we propose a new general method for aggregating crisp values, TFNs, TrFNs and linguistic values into AIFNs. Thus all the group decision matrices for each alternative which involves heterogeneous information are transformed into an Atanassov's intuitionistic fuzzy decision matrix which only contains AIFNs. To determine the attribute weights, a multiple objective Atanassov's intuitionistic fuzzy programming model is constructed and solved by converting it into a linear program. Subsequently, comparison analyses demonstrate that the proposed aggregated technology can overcome the drawbacks of existing methods. An example about cloud computing service evaluation is given to verify the practicality and effectiveness of the proposed method.     

Deriving the personalized individual semantics of linguistic information from flexible linguistic preference relations

In group decision making, flexible linguistic preference relations (FLPRs) are very useful with the pairwise comparisons taking the form of flexible linguistic expressions (FLEs). Due to the fact that different decision makers have different understandings of words, this paper investigates the personalized individual semantics (PISs) of the linguistic information in FLPRs. Two optimization models are constructed to compute a linguistic distribution which is closest to an incomplete FLE. The FLPRs are transformed into fuzzy preference relations by using optimization models which maximize consistency and consensus of the fuzzy preference relations. The PISs of linguistic terms and subsets of the linguistic term set are obtained in this process. A group decision making model based on FLPRs is presented and a green supplier selection problem in automotive industry is solved by using the proposed model. The comparative analysis is presented to show the feasibility of the group decision making model.     

A decision support model for group decision making with intuitionistic fuzzy linguistic preferences relations

As a new preference structure, the intuitionistic fuzzy linguistic preference relation (IFLPR) was introduced to efficiently cope with situations in which the membership degree and non-membership degree are represented as linguistic terms. For group decision making (GDM) problems with IFLPRs, two significant and challenging issues are individual consistency and group consensus before deriving the reliable priority weights of alternatives. In this paper, a novel decision support model is investigated to simultaneously deal with the individual consistency and group consensus for GDM with IFLPRs. First, the concepts of multiplicative consistency and weak transitivity for IFLPRs are introduced and followed by a discussion of their desirable properties. Then, a transformation approach is developed to convert the normalized intuitionistic fuzzy priority weights into multiplicative consistent IFLPR. Based on the distance of IFLPRs, the consistency index, individual consensus degree and group consensus degree for IFLPRs are further defined. In addition, two convergent automatic iterative algorithms are proposed in the investigated decision support model. The first algorithm is utilized to convert an unacceptable multiplicative consistent IFLPR to an acceptable one. The second algorithm can assist the group decision makers to achieve a predefined consensus level. The main characteristic of the investigated decision support model is that it guarantees each IFLPR is still acceptable multiplicative consistent when the predefined consensus level is achieved. Finally, several numerical examples are provided, and comparative analyses with existing approaches are performed to demonstrate the effectiveness and practicality of the investigated model.

     

Algorithm for improving additive consistency of linguistic preference relations with an integer optimization model

Linguistic preference relation (LPR) composed by linguistic terms can well express decision makers’ (DMs’) qualitative preference opinion by comparing alternatives with each other. The investigation of its consistency becomes an important issue to guarantee the rationality of the decision making solutions. Therefore, it is significant to investigate the consistency measure and the consistency improving approach for LPRs. In this paper we present a new method for group decision making (GDM) with LPRs. First, an additive consistency index is introduced on the basis of the information of the original LPR to check whether a LPR is acceptably additive consistency. For unacceptably additively consistent LPR, an integer optimization model is further developed to obtain the acceptably additively consistent LPR. Moreover, the optimization model can guarantee the integrity of the information of the LPR with acceptably additive consistency. Then, with respect to GDM with LPRs, an entropy weight method is proposed to determine the weights of DMs. Finally, the proposed methods are implemented in two numerical examples including a GDM problem. Meanwhile, the comparative analysis with existing methods are discussed in detail to demonstrate the validity of the proposed methods.     

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。     

考虑个体累积共识贡献的犹豫模糊语言自适应共识模型

针对犹豫模糊语言信息下的多属性群决策问题,提出一种基于个体累积共识贡献的自适应共识决策模型.首先,利用犹豫模糊语言得分函数,基于经典的信息熵和相对熵理论,综合考虑同一属性下不同方案间的信息差异,以及各方案分别与正理想方案和负理想方案的信息差异,构建确定属性权重的优化模型;然后,提出个体累积共识贡献测度和全局共识测度,利用全局共识度进行共识控制,依据个体累积共识贡献度对专家权重进行自适应修正,构建一种新的犹豫模糊语言自适应共识过程.该过程的特点是对拥有较少合作的非全共识专家执行专家权重惩罚,而且专家权重的更新引起属性权重的自适应更新,反过来又影响个体共识贡献的累积.最后通过一个应急医疗设施选址的共识决策例子表明方法的可行性和有效性.     

Soft computing based on maximizing consensus and fuzzy TOPSIS approach to interval-valued intuitionistic fuzzy group decision making

Multi-attribute group decision making (MAGDM) is an important research topic in decision theory. In recent decades, many useful methods have been proposed to solve various MAGDM problems, but very few methods simultaneously take them into account from the perspectives of both the ranking and the magnitude of decision data, especially for the interval-valued intuitionistic fuzzy decision data. The purpose of this paper is to develop a soft computing technique based on maximizing consensus and fuzzy TOPSIS in order to solve interval-valued intuitionistic fuzzy MAGDM problems from such two aspects of decision data. To this end, we first define a consensus index from the perspective of the ranking of decision data, for measuring the degree of consensus between the individual and the group. Then, we establish an optimal model based on maximizing consensus to determine the weights of experts. Following the idea of TOPSIS, we calculate the closeness indices of the alternatives from the perspective of the magnitude of decision data. To identify the optimal alternatives and determine their optimum quantities, we further construct a multi-choice goal programming model based on the derived closeness indices. Finally, an example is given to verify the developed method and to make a comparative analysis.