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Social network group decision-making (SNGDM) develops rapidly because of the popularity of online connections among experts. The current SNGDM studies mainly focus on the influence of trust on the evolution of consensus opinions through a complex process. Some situations are ignored in the existing research when trust may negatively affect the decision-making process and trust relationships may be developed or interrupted during consensus negotiation processes. To overcome such limitations, we propose a consensus model based on the trust-consensus multiplex network by combing trust social network analysis and consensus evolution networks (CENs). We design an interaction mechanism between trust and consensus based on the dynamic experts’ influence which is computed by the multiplex PageRank centrality measure, especially focusing on the negative impact of trust on consensus. Besides, we compute consensus levels based on the density and intensity of CENs to determine when should the negotiation end. The proposed model can not only consider the mutual influence between trust and consensus in SNGDM, but also detect and analyze the negative influence of trust on consensus. An example examines the effectiveness of the proposed model and a comparative analysis shows its flexibility for studying the complex consensus situation of SNGDM. [ABSTRACT FROM AUTHOR]

In large-scale group decision making (LSGDM), appropriate clustering analysis is important to consensus reaching since it can reduce the interactive complexity among individuals. According to the traditional clustering method, a conflict may arise between the consensus reaching levels and total adjustment costs within clusters when individuals have different unit adjustment cost, which reflects their willingness to make concessions. Since this conflict may aggravate the consensus complexity, we propose a new $K$ -means clustering method that considers both preferences and the preference adjustment cost. The preference adjustment cost is attached to preferences with a parameter that can be determined by balancing this conflict. Because of such conflict, the proposed clustering algorithm can improve the similarity of intracluster individuals on the preference adjustment cost by offsetting some acceptable consensus reaching levels within clusters. According to the proposed clustering algorithm, individuals who have both similar preferences and adjustment willingness are classified into the same clusters. In this way, the moderator can provide similar compensation strategies for intracluster individuals, which will decrease the adjustment complexity. A practical case study of team construction examines the application of the proposed algorithm, and the related comparative analysis shows that it is convenient for managers to persuade individuals to reach a consensus under the improved clustering results. [ABSTRACT FROM AUTHOR]

In most existing linguistic distribution multiple criteria group decision-making (MCGDM) models, the sample size of group linguistic distribution assessment (LDA) is often neglected, and the decision makers are viewed to be independent. The probabilistic distribution is closely related to the sample size, and there exist more or fewer interference effects among different individual opinions. Thus, this article develops a quantum framework for modeling interference effects in the linguistic distribution MCGDM process. First, considering the sample size information, we redefine the LDAs and provide a new computational model for them. Second, to integrate a series of LDAs, the linguistic distribution weighted averaging (LDWA) operator is presented. Mathematic proofs reveal that the new LDWA operator can not only ensure the information integrality but also can avoid the conjunctive and disjunctive operations. Third, to explore the interference effects among individual opinions, a quantum framework is constructed. In this process, individual opinions are viewed as various wave functions occurring synchronously. They interfere with each and influence the aggregation result. Finally, an illustrative example of Internet finance soft power evaluation is provided to verify the effectiveness. Sensitivity and comparative analyses are also implemented to assess the stability and validity of our method. [ABSTRACT FROM AUTHOR]

Ranking of fuzzy numbers (FNs) is a key stage within fuzzy multicriteria decision analysis (FMCDA). However, the influence of FNs dependence on their ranking, including ranking alternatives within FMCDA, has not been studied yet. In this article, for studying such an influence, the widely used defuzzification-based fuzzy ranking methods, centroid index, and integral of means, along with their modifications, which are pairwise comparison defuzzification ranking methods, are explored. The authors argue that classical defuzzification ranking methods are intended to deal with independent FNs, whereas their modifications may be used for ranking of dependent FNs. It is provided a proof in which, pairwise comparison Yuan’s and defuzzification integral of means ranking methods, are equivalent when ordering independent and can differ when ordering dependent FNs; at the same time, Yuan’s and modified integral of means ranking methods are equivalent when ordering both independent and dependent FNs. Intransitivity of the two modified ranking methods when ordering dependent FNs as well as intransitivity of alternatives in FMCDA for fuzzy multiattribute value theory (FMAVT) as an example is proved. The distinctions in ranking of dependent FNs by all ranking methods under consideration are explored through ordering alternatives within FMAVT. For this, a real-life case study is considered, and the distinctions in ordering alternatives by classical and modified ranking methods are demonstrated. Statistical analysis of distinctions in ordering alternatives by FMAVT with different ranking methods is implemented with the use of Monte–Carlo simulation. The significance of distinctions for the choice and ranking multicriteria problems, as well as for justification of utilizing ranking methods under consideration in FMCDA, is discussed. [ABSTRACT FROM AUTHOR]

In this article, we propose the concept of flexible linguistic preference relations (FLPRs), in which the flexible linguistic expressions, a more flexible way to form linguistic expressions, are employed. Further, we present a method to rank alternatives based on preference information in FLPRs by exploring the linguistic distribution (LD) and priority-based approximation (PA) of FLPRs. In the LD-based approximation, we first present a two-stage optimization process to approximate FLPRs to distribution linguistic preference relations (DLPRs) following the principles of minimum preference loss and maximum consistency. Then in the PA process, we derive priority vectors from the DLPRs with some desired properties. Finally, a comparative analysis of the priority vectors derived from different kinds of linguistic preference relations is presented to illustrate our proposal. [ABSTRACT FROM AUTHOR]

Large-scale group decision-making (LSGDM) solution is usually based on the clustering analysis process (CAP) and consensus reaching process (CRP). However, CAP and CRP can be contradictory since CAP is performed based on the differences between potentially small groups and CRP is conducted to improve the overall similarity of a large group. To balance CAP and CRP, a dynamic clustering analysis process (DCAP) based on consensus evolution networks is proposed. A clustering algorithm proposed based on community detection method can be used to handle the diverse network structures with dynamic consensus thresholds. The clustering validity based on the intracluster consensus levels in subgroups and the intercluster consensus level among subgroups is evaluated. Then, the DCAP after each feedback adjustment round in CRP is reanalyzed. In such a way, effective clustering can also be found after a satisfying consensus is reached. Finally, a case study shows the availability of this approach and comparative analyses are provided to highlight the advantages from both theoretical and numerical perspectives. [ABSTRACT FROM AUTHOR]

In this article, we deal with an improved fusion method for multigranular linguistic distribution assessments, a flexible and practical expression, in a multiple criteria group decision-making problem, which permits an accurate transformation between two linguistic labels without the loss of information. The importance degree of decision makers is allocated on the basis of individual consistency elicited from evaluation assessments represented by linguistic distributions, which is described with the aid of the proposed dominance degree of linguistic distribution. To intuitively reflect the group consensus level, a new measure, Jaccard consensus of linguistic distribution, is introduced. Based on this, a consensus-based multicriteria group preference analysis model with multigranular linguistic distribution information is established within a unified framework, which is developed by means of additive multiattribute value utility theory. Furthermore, a corresponding algorithm is matched to obtain a representative value function for decision analysis and an illustrative example is developed to illustrate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Various linguistic expressions have been presented to model the flexibility of linguistic preference expressions and to support the consensus reaching in linguistic group decision-making (GDM). In this paper, we propose the concept of flexible linguistic expressions (FLEs) as a general linguistic preference expression format to improve the flexibility of the construction of complex linguistic expressions and the elicitation of linguistic preferences and, then, we develop a new linguistic GDM model with FLEs, referred to as FLE-based GDM (FLEGDM). In the FLEGDM, an FLE aggregation process with accurate constraints is developed to improve the quality (i.e., accuracy) of the collective result as well as guarantee the principle of minimum preference-loss through a mixed 0–1 linear programming model. Meanwhile, the consensus rules with minimum preference-loss are designed to support the consensus reaching process (CRS) in the FLEGDM. Finally, we present the detailed comparative analysis involving different linguistic GDM models to show the advantages of the FLEGDM. [ABSTRACT FROM AUTHOR]

Finding the maximum and minimum values of a given collection of real inputs is critical in many decision-making and evaluation models. In often encountered evaluation problems where information is collected based on survey or statistics and embodied by a collection of normalized distributions on lattice, we cannot directly obtain the corresponding concept of “maximum” and “minimum.” To process such situations and related evaluation problem, we first define the distributions poset on a given lattice structure and then propose the concept of lattice dominance points, which can sometimes be seen as a type generalized “maximum” points. Often there may be infinite dominance points to choose from. In order to find some more suitable ones according with our intuition and with mathematical completeness, we propose an optimization method and distribution t-conorm methods to elicit lattice dominances based on given collection of normalized distributions. The distribution and bilinear distribution t-conorms examples are well defined, and some related properties are proposed with strict proofs. In addition, a commonly used evaluation model is proposed with results for comparing differently elicited lattice dominance points. [ABSTRACT FROM AUTHOR]