基于重要度引导偏好识别修正的多粒度语言共识模型

研究多粒度语言偏好信息下的群体共识决策问题. 首先, 从个体和群体两个角度充分挖掘偏好信息下隐含的专家重要度信息, 基于个体一致度及个体与群体的相似度构建确定专家重要度的优化模型; 其次, 以专家重要度引导非共识偏好的识别和修正过程, 提出一种自适应的语言共识模型; 然后, 给出一种群决策方法, 确保在集结专家意见前群体达成一定程度的共识; 最后, 通过算例验证所提出方法的可行性和有效性.

     

多属性群决策达成一致方法研究

在群决策过程中,专家对于候选方案的每个属性都提出自己的个体决策信息.关于专家意见的一致化问题,提出一种迭代算法,能自动完成个体意见的一致化,不需要专家修改决策信息.在群体决策矩阵的基础上,用乘性加权集结算子把方案的属性值进行集结,得到方案的群体综合属性值,从而选出最优方案.详细介绍了算法的实现过程,并用一实际例子说明了算法的可行性.     

基于直觉模糊熵的专家权重确定方法及其验证

针对专家判断信息以直觉模糊集给出的直觉模糊群决策矩阵,提出一种新的客观确定专家权重的方法。与传统的通过专家评价的差异程度来确定专家权重的思路不同,该方法通过定义直觉模糊集的模糊熵计算专家判断信息的模糊程度,进而确定每位专家的权重,并对基于犹豫度、几何距离、相似度量和不确定程度4类模糊熵的定义对专家权重结果的影响进行实验和仿真分析。仿真结果表明,专家的权重不仅取决于不同类模糊熵的定义,还与专家个数和属性个数相关。     

Application of MADM in a fuzzy environment for selecting the best barrier for offshore wells

A fuzzy Multi Attribute Decision Making (FMADM) method, which is suitable for treating group decision making problems in a fuzzy environment, is proposed for ranking offshore well barriers from a cost-benefit view point. It is obvious that much knowledge in the real world is fuzzy rather than precise. MADM decision data is usually fuzzy, crisp, or a combination of the two. A useful model is proposed here in order to handle both fuzzy and crisp data. Imprecision and ambiguity in the calculation of a performance rating are incorporated into MADM whereby fuzzy set theory provides a mathematical framework for modeling them. Human opinions often conflict in group decision-making. The purpose of fuzzy MADM is to aggregate the conflicting opinions. In general, one expert’s opinion for a given attribute may be different from others’. Therefore, it is necessary to develop an appropriate method of aggregating multiple experts’ opinions, taking into account a degree of importance of each expert in the aggregation procedure. The weights of all attributes and experts are estimated using a Fuzzy Analytical Hierarchy Process (FAHP). Finally, the best well barrier or risk control option (RCO) with respect to cost and benefit is selected using a Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method.     

A new approach to fuzzy distance measure and similarity measure between two generalized fuzzy numbers

In this paper a fuzzy distance measure between two generalized fuzzy numbers is developed. The metric properties of this distance measure are also studied. The new distance measure is compared with the other fuzzy distance measures proposed by Voxman [W. Voxman, Some remarks on distances between fuzzy numbers, Fuzzy Sets and Systems 100 (1998) 353–365] and Chakraborty and Chakraborty [C. Chakraborty, D. Chakraborty, A theoretical development on fuzzy distance measure for fuzzy numbers, Mathematical and Computer Modelling 43 (2006) 254–261] and turned out to be more reasonable. A new similarity measure is also developed with the help of the fuzzy distance measure. Examples are given to compare this similarity measure with the other similarity measure previously proposed. A decision making scheme is proposed using this similarity measure and this scheme is found to be more acceptable than the existing methods due to the fact that it considers the degrees of confidence of the experts’ opinion.     

基于共识标准的语言标度颗粒优化模型

研究语言偏好信息下的群决策问题.定义了反映群体共识的两个测度指标,分别反映群体内所有专家的一致性水平及专家的个人观点与群体观点的分歧程度;基于共识测度指标构建一种语言标度的颗粒优化模型,提出了求解语言标度颗粒最佳分界点的改进PSO算法,并给出一种对方案排序进行择优的群决策方法. 最后,通过一个算例说明了所提出方法的可行性和有效性.     

Two flexibility degrees-driven consensus model in group decision making with intuitionistic fuzzy preference relations

A group of experts are commonly invited to find an optimal solution to a complex decision making problem. When the bipolarity of decision information should be considered in group decision making (GDM), intuitionistic fuzzy values (IFVs) have the capability to model such opinions of decision makers (DMs). This paper develops a consensus model in GDM under intuitionistic fuzzy environments with flexibility. First, it is assumed that the initial opinions of DMs are expressed as intuitionistic fuzzy preference relations (IFPRs). A novel additive consistency index is constructed to measure the deviation degree of IFPRs from fuzzy preference relations (FPRs) with additive consistency, where the non-determinacy degree of IFPRs is incorporated. The thresholds of the proposed index corresponding to IFPRs with acceptable additive consistency are discussed and computed. Second, the consensus level of DMs is defined using the similarity degree between two IFVs. An optimization problem is established by maximizing the fitness function, which is constructed by linearly combining the proposed additive consistency index and consensus level. Two flexibility degrees are offered to each DM such that the initial opinions with the bipolarity can be adjusted correspondingly. Third, individual IFPRs in GDM are optimized using the particle swarm optimization (PSO) algorithm. Numerical examples are carried out to illustrate the proposed consensus model by comparing with the existing ones. The obtained results reveal that the proposed additive consistency index can reflect the inherent property of IFPRs. Different with the previous studies, two original flexibility degrees are proposed to characterize the multi-granularity of decision information in GDM.     

Linguistic-labels aggregation and consensus measure for autocratic decision making using group recommendations

Group decision making is a common and important activity in everyday life. In many cases, due to inherent uncertainty, experts cannot express their score or preference using exact numbers. The use of linguistic labels makes expert judgment more reliable and informative for decision-making. One of the problems of group decision making in fuzzy domains is aggregating experts' opinions, expressed using linguistic labels, into a group opinion. This aggregation allows the group to select the most "preferred" alternative from a finite set of candidates. The aggregation of individual judgments into a group opinion requires a measured level of consensus. In this paper, by introducing a new linguistic-labels aggregation operation, we present a procedure for handling an autocratic group decision-making process under linguistic assessments. The methodology presented results in two consequent outcomes: a group-based recommendation, and a score for each expert, reflecting the expert's contribution towards the group recommendation. By changing the weights of the experts based on their contributions, we increase the consensus and reinforce the common decision, without forcing the experts to modify their opinions. This methodology allows an autocratic decision maker to use a diversified group of consultants for a succession of decisions reaching a high level of consensus.     

考虑专家偏好关联的群决策方法及其应用

通过分析群决策过程,提出使用模糊测度描述专家偏好之间可能存在的关联关系,并给出了一种考虑专家偏好关联的群决策方法.该方法从参评专家知识结构的相似性及判断结果的相似性出发,通过计算得到相应的2-可加模糊测度来描述专家的重要程度,并使用Choquet积分将多个专家的偏好信息聚合为群体的判断结果.最后,通过一个潜艇装备论证的例子验证了所提出方法的可行性和合理性.     

A flexible consensus scheme for multicriteria group decision making under linguistic assessments

The present paper proposes a flexible consensus scheme for group decision making, which allows one to obtain a consistent collective opinion, from information provided by each expert in terms of multigranular fuzzy estimates. It is based on a linguistic hierarchical model with multigranular sets of linguistic terms, and the choice of the most suitable set is a prerogative of each expert. From the human viewpoint, using such model is advantageous, since it permits each expert to utilize linguistic terms that reflect more adequately the level of uncertainty intrinsic to his evaluation. From the operational viewpoint, the advantage of using such model lies in the fact that it allows one to express the linguistic information in a unique domain, without losses of information, during the discussion process.The proposed consensus scheme supposes that the moderator can interfere in the discussion process in different ways. The intervention can be a request to any expert to update his opinion or can be the adjustment of the weight of each expert’s opinion. An optimal adjustment can be achieved through the execution of an optimization procedure that searches for the weights that maximize a corresponding soft consensus index.In order to demonstrate the usefulness of the presented consensus scheme, a technique for multicriteria analysis, based on fuzzy preference relation modeling, is utilized for solving a hypothetical enterprise strategy planning problem, generated with the use of the Balanced Scorecard methodology.     

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.     

An adaptive group decision making framework: Individual and local world opinion based opinion dynamics

Opinion dynamics (OD) models, which simulate individuals’ opinion evolution process on social network to analyze the final state of opinion distribution in a group, usually differ from each other due to the differences in social network evolution rules and opinion evolution rules. However, most existing social network evolution rules and opinion evolution rules usually cannot characterize the comprehensive influence of key factors such as neighbors and opinion differences in social relationships. To fully consider the properties of social network evolution and improve the efficiency of consensus reaching process in group decision making, this paper introduces the concept of local world opinion derived from individuals’ common friends, and then proposes an individual and local world opinion-based OD model. In the proposed model, social network evolution is jointly determined by the distance between individual opinions and network structure similarity. The pair of individuals with the largest consensus improvement space are then suggested to adjust their opinions by using an adaptive individual opinion adjustment mechanism. Finally, detailed simulation results are provided to demonstrate the convergence of the proposed model and analyze different parameters’ effects on the stabilized time steps and the number of stable state opinion clusters.     

Multi-step ranking of alternatives in a multi-criteria and multi-expert decision making environment

In this work we introduce a decision model, in the form of a recursive aggregation algorithm, that attempts to mimic a multi-step ranking process of a set of alternatives in a multi-criteria and multi-expert decision making environment. The main idea is rather intuitive. Each alternative is initially assigned a list of values, representing the group experts’ opinion about the extent to which the alternative satisfies a set of given criteria. Then the values for each alternative are combined with the weighted mean operator according to vectors of weights, one for each decision maker in the group. These weights express the personal judgement of the decision makers about the relative importance of the individual criteria. Consequently, a new vector of values is obtained for each alternative. These new values are combined again with the weighted mean operator taking into account the different degrees of influence each decision maker accepts from the rest of the group. The latter aggregation step is repeated again and again for each alternative until a consensus is attained.     

基于信息熵的专家聚类赋权方法

鉴于群组决策专家赋权方法研究中,现有赋权方法虽然考虑了专家给出的排序向量的一致性,但缺乏对排序向量信息相似性的度量,导致可能出现排序向量与群体共识相近,但信息不确定性较大的专家被赋予了与其他专家相同权重的问题.基于此,提出一种基于信息熵的专家聚类赋权方法,运用信息相似系数对排序向量进行聚类分析,根据聚类结果和排序向量的...     

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.

     

An integrated decision model for evaluating educational web sites from the fuzzy subjective and objective perspectives

With advances in information and network technologies, lots of data have been digitized to reveal information for users by the construction of Web sites. Unfortunately, they are both overloading and overlapping in Internet so that users cannot distinguish their quality. To address this issue in education, Hwang, Huang, and Tseng proposed a group decision system to evaluate the quality of educational Web sites by users’ and experts’ opinions. Their investigative source is solely stemmed from human intention, called the subjective perspective, to make judgments on the quality of Web sites. However, the nature of human beings in making decisions has a gap between intention and behavior. Asking people for eliciting thought is arduous to cause this gap. Human behavior, namely the objective perspective, is the other essential source to obtain human thinking and real doings. For this reason, we can use data mining approaches to acquire the objective source. In this research, we propose an integrated decision model applied in evaluating educational Web sites from the fuzzy subjective and objective perspectives. The former source is extracted by inquiring human opinion using a questionnaire, while the latter is gained automatically by a data mining technique, fuzzy clustering. An empirical study is carried out to validate the model capability.     

Modeling the concept of majority opinion in group decision making

In this paper the problem of group decision making is studied. One of the main issues in this context is to define a decision strategy which takes into account the individual opinions of the decision makers. The concept of majority plays in this context a key role: what is often needed is an overall opinion which synthesizes the opinions of the majority of the decision makers. The reduction of the individual values into a representative value (which we call the majority opinion) is usually performed through an aggregation process. Within fuzzy set theory the concept of majority can be expressed by a linguistic quantifier (such as most), which is formally defined as a fuzzy subset. In this paper we propose two distinct approaches to the definition of a majority opinion. We first consider the case where linguistic quantifiers are associated with aggregation operators which allow us to compute a majority opinion by aggregating the individual opinions. In this case the majority opinion corresponds to the aggregated value. To model this semantics of linguistic quantifiers the IOWA operators are used and a new proposal of definition of their weighting vector is presented. A second method is based on the consideration of the concept of majority as a vague concept. Based on this interpretation we propose a formalization of a fuzzy majority opinion as a fuzzy subset.     

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.     

A GRA-based intuitionistic fuzzy multi-criteria group decision making method for personnel selection

Due to the increasing competition of globalization, selection of the most appropriate personnel is one of the key factors for an organization’s success.The importance and complexity of the personnel selection problem call for the method combining both subjective and objective assessments rather than just subjective decisions. The aim of this paper is to develop a new method for solving the decision making process. An intuitionistic fuzzy multi-criteria group decision making method with grey relational analysis (GRA) is proposed. Intuitionistic fuzzy weighted averaging (IFWA) operator is utilized to aggregate individual opinions of decision makers into a group opinion. Intuitionistic fuzzy entropy is used to obtain the entropy weights of the criteria. GRA is applied to the ranking and selection of alternatives. A numerical example for personnel selection is given to illustrate the proposed method finally.     

Consensus model for large-scale group decision making based on fuzzy preference relation with self-confidence: Detecting and managing overconfidence behaviors

With the development of intelligent decision-making, one kind of decision modes involves a large number of decision-makers (DMs), which is called large scale group decision making (LSGDM). In LSGDM, overconfidence is one of the common behaviors because of many DMs’ participation and the bounded rationality of human decision. Overconfidence usually has a negative impact on LSGDM and can even lead to failure in the final decision(s). To achieve consensus is very important for LSGDM. Different consensus models of LSGDM have been proposed, while the DMs’ overconfidence behaviors in the consensus have not been concerned. Hence, the purpose of this paper is to propose a consensus model which considers overconfidence behaviors, and the paper mainly focuses on LSGDM based on fuzzy preference relations with self-confidence (FPRs-SC). In the proposed model, a DM clustering method, which combines fuzzy preference values similarity and self-confidence similarity, is used to classify the DMs with similar opinions into a subgroup. A group consensus index which considers both the fuzzy preference values and self-confidence is presented to measure the consensus level among DMs. An overconfidence measurement is given to detect the DMs’ overconfidence behaviors in the consensus. Subsequently, the detailed overconfidence behavior analysis is presented involving two aspects: fuzzy preference values consensus and self-confidence consensus. A dynamic weight punishment mechanism is implemented for overconfident DMs to improve the consensus efficiently. The effectiveness and advantages of the presented consensus model are validated by a numerical example and comparative analysis.