Multi-attribute group decision making with opinion dynamics based on social trust network

Social trust network (STN) has facilitated information exchange between experts during interactions. Some feedback mechanisms have been used to provide advices for opinion change to improve their consensus levels. However, they do not consider the experts’ willingness and their self-confidence values. To analyze the influence of the relationship between experts on the decision-making results, this paper proposes a multi-attribute group decision making (MAGDM) with opinion dynamics based on STN. Three stages are included in the proposed approach: trust propagation, consensus reaching process and alternative selection. In the trust propagation stage, the social weight influence matrix and the weights of experts are obtained based on the complete social trust matrix which is constructed by trust aggregation and the given self-confidence values of experts. In the consensus reaching process, the consensus measure is used to determine the consensus between the experts or not, and the feedback mechanism based on opinion dynamics is used to adjust the opinions which do not reach consensus. The appropriate alternative is selected based on the assessable value of the alternative in the selection process. Finally, a numerical experiment about supplier selection is introduced to illustrate the efficiency of the proposed approach and comparison analyses show that the proposed approach can improve efficiency compared with the MAGDM in the social network.     

Trust based consensus model for social network in an incomplete linguistic information context

A theoretical framework to consensus building within a networked social group is put forward. This article investigates a trust based estimation and aggregation methods as part of a visual consensus model for multiple criteria group decision making with incomplete linguistic information. A novel trust propagation method is proposed to derive trust relationship from an incomplete connected trust network and the trust score induced order weighted averaging operator is presented to aggregate the orthopairs of trust/distrust values obtained from different trust paths. Then, the concept of relative trust score is defined, whose use is twofold: (1) to estimate the unknown preference values and (2) as a reliable source to determine experts’ weights. A visual feedback process is developed to provide experts with graphical representations of their consensus status within the group as well as to identify the alternatives and preference values that should be reconsidered for changing in the subsequent consensus round. The feedback process also includes a recommendation mechanism to provide advice to those experts that are identified as contributing less to consensus on how to change their identified preference values. It is proved that the implementation of the visual feedback mechanism guarantees the convergence of the consensus reaching process.     

A maximum self-esteem degree based feedback mechanism for group consensus reaching with the distributed linguistic trust propagation in social network

This paper focuses on consensus reaching process (CRP) under social network in which the trust relationship expressed by linguistic information. A new feedback mechanism in social network group decision making (SN-GDM) is proposed, which mainly consists of the following two aspects: (1) The propagation of distributed linguistic trust is investigated to study trust relation among experts; (2) A maximum self-esteem degree based feedback mechanism is developed to produce personalized advice for reaching higher group consensus. To do so, a novel linguistic trust propagation method is proposed to obtain the complete trust relationship among group. The self-esteem degree is used to define the extent that an individual makes concessions. Then, a maximum self-esteem degree based optimal feedback mechanism is built to produce personalized advice to help inconsistent experts make change of their opinion. Its novelty lies in the establishment of an optimization model with the nonlinear group self-esteem degree function as the objective function while group consensus threshold as the restrictions. Therefore, the inconsistent experts will reach a group consensus with the minimum loss of self-esteem degree, and then, it achieves the optimal balance between individual self-esteem and group consensus. Finally, a ranking process is applied to derive the appropriate consensus solution.     

A dynamically weight adjustment in the consensus reaching process for group decision-making with hesitant fuzzy preference relations

The consensus reaching process is a dynamic and iterative process for improving group's consensus level before making a final decision in group decision-making (GDM). As the experts will express their opinions under their own intellectual level from different aspects, it is natural that the experts’ weights should reflect their judgment information. This paper proposes a dynamic way to adjust weights of decision-makers (DMs) automatically when they are asked to give original judgment information for GDM problems, in which the DMs express their judgment information by hesitant fuzzy preference relations (HFPRs). Two indices, an individual consensus index of hesitant fuzzy preference relation (ICIHFPR) and a group consensus index of hesitant fuzzy preference relation (GCIHFPR), are introduced. Normalisation of HFPRs with different numbers of possible values is taken into consideration for better computation and comparison. An iterative consensus reaching algorithm is presented with DMs’ weighting vector changing in each consensus reaching process and the process terminates until both the ICIHFPR and GCIHFPR are controlled within predefined thresholds. Finally, an example is illustrated and comparative analyses demonstrate the effectiveness of the proposed methods.     

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.     

A discrete consensus support model for multiple attribute group decision making

In multiple attribute group decision making (MAGDM), it is preferable that the set of experts reach a high degree of consensus amongst their opinions before applying a selection process. In this paper, we present a discrete model to support the consensus reaching process for MAGDM problems. Firstly, a consensus scheme for a set of arguments is provided, where the basic idea is to tighten the range of opinions amongst experts. Based on the well-defined scheme, a convergent algorithm is presented to autocratically guide experts to reach a predefined consensus level. In the selection process, the maximizing deviation method is applied to determine the attribute weights. Then, the choice of the best alternative(s) from the group decision matrix is obtained by the simple additive weighting method. Finally, one example is presented to show the application and effectiveness of the proposed model.     

A consensus‐ and harmony‐based feedback mechanism for multiple attribute group decision making with correlated intuitionistic fuzzy sets

In this study, an interactive consensus model is proposed for correlated multiple attribute group decision making (MAGDM) problems with intuitionistic triangular fuzzy numbers (ITFNs). The harmony degree (HD) is investigated to determine the degree of maintaining experts' original information while the consensus level is defined as the proximity degree (PD) between an expert and other experts on three levels: evaluation elements of alternatives, alternatives, and decision matrices. Combining HD and PD, a three‐dimensional feedback mechanism is proposed to identify discordant experts, alternatives, and corresponding preference values that contribute less to consensus, and provides advice to reach a higher consensus level. Additionally, visual representation of experts' consensus position within the group is provided. Furthermore, a graphical simulation of future consensus and harmony status, if the recommended values were to be implemented, is also provided. Therefore, our proposed feedback mechanism guarantees that it increases the consensus level of the set of experts while maintaining, as much as possible, experts' original information. Then, the PD‐induced intuitionistic triangular fuzzy correlated averaging (PD‐IITFCA) operator is investigated to aggregate the interactive individual opinions between experts. Finally, the intuitionistic triangular fuzzy correlated averaging (ITFCA) operator is developed to aggregate the evaluation elements of alternatives under correlative attributes. Based on the score and accurate functions of ITFNs, an order relation is proposed to obtain the final solution of alternatives.     

The interactive consensus reaching process with the minimum and uncertain cost in group decision making

The consensus model with the minimum cost (or minimum adjustments or minimum information loss) is a powerful decision tool for consensus building in the group decision making (GDM). In the extant consensus models with the minimum cost, the unit adjustment cost of each expert is assumed to be exactly known, and an optimization-based consensus model is utilized to support the consensus building. In the practical GDM, however, it is difficult to obtain the exact unit adjustment costs, and the unit adjustment costs of experts are often uncertain. Moreover, we argue that the consensus cannot be achieved directly using the established optimization-based consensus model, because the consensus building is an interactive process that needs the participation of experts. This paper proposes an interactive consensus reaching process with the minimum and uncertain cost. In the consensus reaching process, an optimization-based consensus model with the uncertain unit cost is constructed to obtain the optimal adjusted opinions of experts. Then, the costs/resources are provided for experts to modify their opinions, and the obtained optimal adjusted opinions are used as a reference for the opinions-modifying in the consensus reaching process. Meanwhile, the unit adjustment costs of experts can be estimated according to the actual situation of the opinions-modifying in the consensus reaching process. The detailed numerical and simulation analysis are conducted to demonstrate the validity of the proposed consensus reaching model.     

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.     

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.     

Adaptive consensus support model for group decision making systems

In this paper, we present an adaptive consensus support model for group decision making systems based on intervals of linguistic 2-tuples. The proposed method has the following advantages: (1) the evaluating values can either be represented by linguistic terms or intervals of linguistic terms, (2) if the required consensus degree is too high, then the proposed adaptive consensus support model can modify experts’ preferences to improve convergence toward a higher consensus degree or a sufficient agreement for group decision making and (3) the proposed method is an interactive method, where each expert can modify the adjustments made by the system during the consensus reaching process if he/she does not agree with the adjustments made by the system. The proposed adaptive consensus support model can overcome the drawback of Mata et al.’s method (2009). It provides us with a useful way for adaptive consensus support for group decision making based on intervals of linguistic 2-tuples.     

基于模糊判断矩阵的两阶段群决策方法

针对多属性群决策问题,提出一种两阶段决策分析方法。通过分析积型模糊一致性判断矩阵和模糊判断矩阵的排序向量之间的偏差,建立并求解一个规划模型,得到专家模糊判断矩阵的排序向量。由最小化专家模糊判断矩阵的排序向量与专家群组排序向量的偏差,再次建立并求解一个规划模型,得到反映专家群组偏好的排序向量,从而得出基于模糊判断矩阵的两阶段群决策方法。通过2个算例说明了该方法的可行性与有效性。     

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.     

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.

     

专家交互情境下不完备群组DEMATEL决策方法

为克服现有群组DEMATEL存在的尚未考虑群组专家之间的信息交互、对于不完备专家判断信息的推断机理不明确等缺陷,基于社交网络中的信任关系理论和凝聚层次聚类理论,通过给出不完备群组DEMATEL初始直接影响矩阵残缺值的推断方法和专家交互情境下群组DEMATEL直接影响矩阵信息修正方法,提出专家交互情境下不完备群组DEMATEL决策方法的实现步骤.最后,通过算例对比分析反映出通过专家多轮次交互,群组专家之间的共识度以及决策结果的可靠性持续提升,从而验证了所提出方法的科学性和可行性.     

Consistency and consensus reaching process for group decision making based on complete interval distributed preference relations under social network analysis

Group decision-making (GDM) problems often consist of many indeterminacy factors in realistic situation. How to cope with consistency and consensus under uncertain circumstance are two critical issues in pairwise comparison based GDM problems. In this paper, we firstly propose the model of complete interval distributed preference relation (CIDPR) based on the concept of linguistic distribution with interval symbolic proportions, distribution linguistic preference relation (DLPR) and IDPR. Secondly, the additive consistency index of CIDPR is defined to measure the consistency level of expert's judgment, and an adjustment algorithm is proposed for converting inconsistent CIDPR to an acceptable consistent level. Thirdly, since trust relation is a critical factor in the generation of experts’ weights and the adjustment of experts’ opinions, consensus reaching process (CRP) is designed to take into account distributed linguistic trust relations under social network analysis (SNA). In the proposed adjustment mechanism, non-consensus individual should modify opinion towards his/her trusted and highly weighted expert. The advantage of the proposed inconsistent CIDPR adjustment model can maximally retain the information in the original distribution, while the CRP has a relatively fast convergent speed and good practicality. An illustrative example of strategic new product selection is conducted to demonstrate the applicability of the proposed method and its potential in supporting realistic GDM problems.     

Consensus reaching for group decision making with multi-granular unbalanced linguistic information: A bounded confidence and minimum adjustment-based approach

In group decision making problems, there exist the situations that decision makers may use unbalanced linguistic term sets that are not uniformly and symmetrically distributed to provide their linguistic assessments over alternatives. Moreover, due to the difference in knowledge and culture backgrounds, it is also possible that multi-granular linguistic term sets may also be used by decision makers. How to manage multi-granular unbalanced linguistic information in consensus-based group decision making has becoming an important topic in linguistic decision making. In this paper, we first revise Herrera’s unbalanced linguistic term sets and propose a simplified linguistic computational model to fuse multi-granular unbalanced linguistic terms. Afterwards, for multi-criteria group decision making problems with multi-granular unbalanced linguistic information, we develop two optimization models to generate adjustment advice for decision makers who have to change his/her opinions in consensus reaching process, which consider both the bounded confidence levels and minimum adjustment of decision makers’ linguistic assessments. Moreover, an algorithm is further proposed to help decision makers reach consensus in group decision making. Eventually, an application example for ERP system supplier selection and some simulation results are presented to illustrate and justify the consensus reaching algorithm.     

A Consensus Model for Group Decision Making With Incomplete Fuzzy Preference Relations

Two processes are necessary to solve group decision making problems: A consensus process and a selection process. The consensus reaching process is necessary to obtain a final solution with a certain level of agreement between the experts; and the selection process is necessary to obtain such a final solution. In a previous paper, we present a selection process to deal with group decision making problems with incomplete fuzzy preference relations, which uses consistency measures to estimate the incomplete fuzzy preference relations. In this paper we present a consensus model. The main novelty of this consensus model is that of being guided by both consensus and consistency measures. Also, the consensus reaching process is guided automatically, without moderator, through both consensus and consistency criteria. To do that, a feedback mechanism is developed to generate advice on how experts should change or complete their preferences in order to reach a solution with high consensus and consistency degrees. In each consensus round, experts are given information on how to change their preferences, and to estimate missing values if their corresponding preference relation is incomplete. Additionally, a consensus and consistency based induced ordered weighted averaging operator to aggregate the experts' preferences is introduced, which can be used in consensus models as well as in selection processes. The main improvement of this consensus model is that it supports the management of incomplete information and it allows to achieve consistent solutions with a great level of agreement.     

An influence-driven feedback system for preference similarity network clustering based consensus group decision making model

Consensus group decision making (CGDM) allows the integration within this area of study of other advanced frameworks such as Social Network Analysis (SNA), Social Influence Network (SIN), clustering and trust-based concepts, among others. These complementary frameworks help to bridge the gap between their corresponding theories in such a way that important elements are not overlooked and are appropriately taken into consideration. In this paper, a new influence-driven feedback mechanism procedure is introduced for a preference similarity network clustering based consensus reaching process. The proposed influence-driven feedback mechanism aims at identifying the network influencer for the generation of advices. This procedure ensures that valuable recommendations are coming from the expert with most similar preferences with the other experts in the group. This is achieved by adapting, from the SIN theory into the CGDM context, an eigenvector-like measure of centrality for the purpose of: (i) measuring the influence score of experts, and (ii) determining the network influencer. Based on the initial evaluations on a set of alternatives provide by the experts in a group, the proposed influence score measure, which is named the σ-centrality, is used to define the similarity social influence network (SSIN) matrix. The σ-centrality is obtained by taking into account both the endogenous (internal network connections) and exogenous (external) factors, which means that SSIN connections as well as the opinion contribution from third parties are permitted in the nomination of the network influencer. The influence-driven feedback mechanism process is designed based on the satisfying of two important conditions to ensure that (1) the revised consensus degree is above the consensus threshold and that (2) the clustering solution is improved.     

AHP中群决策的几何平均超传递近似法

研究了层次分析法（AHP）群决策中判断矩阵的合并问题.首先,论证了层次分析法中m个判断矩阵的几何平均矩阵是判断矩阵,以及m个判断矩阵的加权几何平均复合判断矩阵是判断矩阵;然后,提出了层次分析法中简化的超传递近似法及群决策的几何平均超传递近似法,该方法不需要一致性检验,同时又保持了专家的原始意见;最后,通过一个实例验证了该方法的有效性和实用性.