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In minimum cost consensus problems, to accomplish the group consensus, decision makers accommodate their initial discrepant opinions based on the unit adjustment costs. During this process, decision makers may exhibit loss aversion, which results in extra expenses when participants feel loss in contrast to their reference opinion adjustments. Existing minimum cost consensus models pay little attention to the loss-averse preference. Hence, to fill up this gap, a minimum cost consensus model with loss aversion (MCCM-LA) is established and the desired properties are analyzed. To manage large-scale group decision making problems, we first propose an integrated opinion similarity, connectivity similarity and behavior similarity clustering algorithm to divide decision makers into multiple subgroups. Balancing the individual adjustment willingness and consensus reaching efficiency, a two-stage consensus reaching mechanism is further designed based on MCCM-LA to realize the accordant opinion. Finally, the effectiveness and feasibility of the proposed method are demonstrated by sensitivity and comparative analyses with an illustrative example. [ABSTRACT FROM AUTHOR]

In the elicitation of decision makers' fuzzy and uncertain assessments, linguistic terms are natural and efficient as the preference modeling tools. Although the linguistic variables are available, they would not be operational without any detailed quantification. Motivated by the flexibility of information granularity, this paper develops information granules to represent linguistic terms in the form of intervals and interval type-2 fuzzy sets (IT2FSs) in best worst method (BWM). The development is aimed at minimizing inconsistency in the decision making (DM) process to ensure the rationality of the assessments provided by decision makers. Furthermore, the input and output based consistencies of BWM are considered. The granulation of entries of pairwise comparison vectors are the foundation of BWM to formulate an optimization problem where particle swarm optimization (PSO) algorithm serves as the optimization framework. Both individual and group decision making (GDM) scenarios are taken into consideration. For the GDM process, a performance index for measuring the group consensus is also proposed. Several examples and validity analysis are covered to illustrate the major ideas of this study. Finally, as a case study, a recommendation of the sequence of visiting tourist attractions in Wuhan and the corresponding comparative analysis are represented. • A granular computing-based method in BWM framework is proposed. • Construction of granular linguistic information to represent preference information of DMs is given. • A novel Euclidean distance function to measure the agreement among the group is proposed. • A case study of scenic spots recommendation in Wuhan with online reviews is exhibited. [ABSTRACT FROM AUTHOR]

In group decision-making processes, decision makers may have different risk preference types, which usually make them take various responses to the same problem. In minimum cost consensus problems, risk seekers, risk neutrals and risk averters may exhibit individual cost adjustment characteristics, which require aggregating their opinions in a model. To solve this problem, this paper presents a minimum cost consensus model to obtain group consensus preferences using a general optimization model, which can handle three types of risk preferences in decision making. In addition, a data-driven weighting scheme for the degrees of importance of decision makers is developed, and a generalized group consensus opinion aggregation function is designed. The proposed group consensus opinion aggregation function extends the existing developed opinion production method, which is more compatible than other aggregation functions. Finally, the proposed minimum cost consensus with risk preferences model is verified through an illustrative example. [ABSTRACT FROM AUTHOR]

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]

Large-scale group decision-making problems based on social network analysis and minimum cost consensus models (MCCMs) have recently attracted considerable attention. However, few studies have combined them to form a complete decision-making system. Accordingly, we define the satisfaction index to optimize the classical MCCM by considering the effect of the group on individuals. Similarly, we define the consistency index to optimize the consensus reaching process (CRP). Regarding the evolution of the consensus network, the Louvain algorithm is used to divide the entire group into several subgroups to ensure that each subgroup is independent but has strong cohesion. By constructing the MCCM based on the satisfaction index and the optimized consensus-reaching process, the group opinions in each subgroup are ranked to obtain the final ranking of alternatives. Finally, to verify the validity of CRP and the practical value of the proposed model, we conduct consensus network evolution and decision-making analysis in the case of a negotiation between the government and polluting companies to achieve uniform pollution emissions. Sensitivity analysis is performed to demonstrate the stability of the subgroup weights. Furthermore, a comparative analysis using existing models verifies the effectiveness of the proposed model. • A new framework of MCCM for LSGDM problems is proposed. • The satisfaction index is defined and used to optimize the MCCM. • The CRP-driven optimization model based on the consistency index is provided. • A new method based on community detection is employed to measure the clustering result. • A case of pollution emissions is conducted to simulate the network evolution. [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 work, we propose some two-layer preference models that can be appropriately applied in management problems such as the group decision making about predicting the future market share of certain product. By introducing the convex IOWA operator paradigm and some related properties and definitions, we list some detailed preference and inducing preference models to demonstrate and exemplify the proposed conceptual frame of two-layer preference model. The convex IOWA operator paradigm facilitates the modeling process and, from mathematical view, makes it stricter. When relevant inducing information and aggregation selection change, the proposed models can be easily adapted to accommodate more different applications in decision making and evaluation. [ABSTRACT FROM AUTHOR]

Interval 2-tuple linguistic model is widely applied to group decision making owing to the representation capabilities.In order to deal with the problem of different labels (multi-granularity), an interval 2-tuple transformation function is developed, which is beneficial to information aggregation and fusion. In addition, a novel and flexible interval 2-tuple ranking function is introduced, which can obtain the ranking result in a single-step procedure. Based on the previous distance measures, the normalized generalized interval 2-tuple distance is proposed. Furthermore, an interval 2-tuple with the aid of TODIM method is introduced to select green suppliers. Finally, a sensitivity analysis is completed and a comparative analysis is carried out with interval 2-tuple TOPSIS and VIKOR methods to verify the validity of the proposed method. [ABSTRACT FROM AUTHOR]

The eruption of COVID-19 at the beginning of 2020 has sounded the alarm, making experts pay more attention to public health emergency events. A suitable emergency response plan plays a vital role in handling emergency events. Therefore, this paper focuses on the evaluation of emergency response plans among a set of group in the comprehensive prospect, and an emergency decision making method integrated with the interval type-2 fuzzy information based on the third generation prospect theory (PT 3) and the extended MULTIMOORA method is proposed. Individuals express their preferences using some given linguistic terms set. Furthermore, considering the conflicts may occur in the group, a convergent iterative algorithm is designed for group consensus reaching. Then, the stochastic multi-criteria acceptability analysis (SMAA) method and the Borda Count (BC) method are generated to combine the results instead of the dominance theory in MULTIMOORA system. Finally, based on the background of the COVID-19 pandemic from Wuhan, a case study about the selection of emergency response plan and the corresponding sensitivity and comparative analysis are exhibited to explain the effectiveness of the proposed method. • A new fuzzy MCDA method to evaluate emergency response plans is proposed. • An integrated model based on PT3 and extended MULTIMOORA with IT2FSs is developed. • The proposed method considers CRP with an effectiveness iterative algorithm. • A case study of emergency response plans assessment on COVID-19 in Wuhan is presented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a method based on Choquet integral is proposed to solve the interval intuitionistic fuzzy multiple attribute group decision making problems. Firstly, some concepts about interval intuitionistic fuzzy measure are defined, through the strict mathematical reasoning to prove the measure we proposed satisfying the axiomatic system of fuzzy measure. Then, on the basis of fuzzy measure and game theory, we propose two models to determine fuzzy measure based on interval intuitionistic fuzzy entropy and weight information matrix. By calculating the Shapely value to determine expert weights, we establish a linear programming model based on relative entropy to determine the fuzzy measure of attribute weights to reflect the interactive characteristics among the criteria, using the Choquet integral to aggregate the decision-making information. Finally, we give the process of decision making in details. [Copyright &y& Elsevier]

In most existing multi-criteria group decision making (MCGDM) problems, the decision makers (DMs) are usually regarded as independent and DMs' psychological behaviors are rarely considered. However, in many cases, the opinions of DMs are likely to influence each other and the DMs often hold subjective bounded rationality in the decision making process. To address this issue, a linguistic distribution behavioral MCGDM model integrating extended generalized TODIM (an acronym in Portuguese of interactive and multi-criteria decision making) method and quantum decision theory is developed. First, linguistic distribution assessments considering the sample size information are used to gather the group linguistic evaluations, which can integrally depict the quantitative distribution and qualitative vagueness. Second, an extended generalized linguistic distribution TODIM method is presented to reflect the DMs' bounded rational behaviors. It is used to calculate the dominance of each alternative. Third, a quantum possibilistic aggregation framework is constructed to explore the interference effects among DMs' opinions. In this process, DMs' opinions are viewed as synchronously occurred wave functions that interfere with each other and influence the aggregated result. Finally, a case study is examined to recommend the optimal automobile for customers based on distributed online reviews in newcar.xcar.com and autohome.com. Three separate scenarios with conjunctive, neural, and disjunctive modes are considered respectively. The sensitivity analysis is given to show the effect of risk factors and interference factors. The parameters show to be dominant in the final best automobile recommendation. The comparisons with some existing methods confirm the validity and stability of the proposed MCGDM method. • Develop a novel linguistic distribution behavioral MCGDM model. • Integrate the generalized TODIM method and quantum decision theory. • Explore the interference effects among DMs' opinions in a quantum framework. • Apply the proposed model to the online automobile recommendation. [ABSTRACT FROM AUTHOR]

• Construct consensus evolution networks (CENs) managing consensus thresholds. • Introduce new consensus index numerically and structurally based on CENs. • Design a pairwise adjustment method based on the complementary sensitive CEN. • Give reference for the agreed consensus threshold based on the sparsity of CENs. The consensus reaching process (CRP) is a critical part of group decision making (GDM). In order to explore the evolution of consensus, a new CRP tool is proposed based on consensus evolution networks (CENs). The CENs are built based on the consensus degrees among decision makers (DMs) and allow us to manage the consensus thresholds and its evolution. A new consensus index is introduced based on the structured and numerical aspects of the CENs. The new consensus index can not only deeply analyze the constitution of consensus, but also determine the weights of DMs. According to the clustering coefficient, the sensitive consensus threshold is identified and the sensitive consensus evolution network (SCEN) is built. Based on the complementary SCEN, a pairwise feedback adjustment method is proposed to improve consensus. Besides, the sparsity of the CENs can act as a reference to determine the agreed consensus thresholds, which is considered an important issue in traditional models. A numerical example is used to verify the usefulness of the proposed CRP tool. The numerical results show that the evolution of consensus can be clearly found based on CENs and the pairwise method can improve consensus in only four rounds. [ABSTRACT FROM AUTHOR]