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Due to the limited knowledge, experience and ability of a single expert, an increasing number of practical multi-criteria sorting (MCS) problems require the participation of multiple experts, which are called MCS problems in the context of group decision-making (MCS-GDM problems for short). To obtain consensual sorting results for alternatives, consensus reaching processes need to be considered in MCS-GDM problems. In this paper, two consensus-based TOPSIS-Sort-B algorithms are developed to deal with MCS-GDM problems. We first develop a minimum adjustment optimization model to obtain consensual boundary profiles by considering different experts’ boundary profiles. Based on individual decision matrices and the collective decision matrix, individual and group sorting results of alternatives can be obtained by using the TOPSIS-Sort-B method, respectively. Afterwards, different local adjustment strategy-based feedback adjustment mechanisms that can meet different needs are proposed to help experts adjust their assessments, and two consensus-based TOPSIS-Sort-B algorithms are designed to obtain consensual sorting results for MCS-GDM. Finally, a numerical example for green building rating and detailed simulation experiments are presented to justify the proposed algorithms and compare different feedback adjustment mechanisms.

In the past 10 years, a large number of consensus-reaching approaches for group decision making (GDM) have been proposed. While these methods either focus on the cost of the consensus reaching or the convergency of the consensus process, the consensus efficiency has long been ignored. Meanwhile, the measurements of consensus threshold are often determined by some subjective and intuitive judgements, such as management experience and estimations for the degree of satisfaction, which lack a theoretical foundation. In management applications, how to measure consensus and how to evaluate a consensus reaching method are also ambiguous. To tackle these questions, we introduce efficiency measures into the consensus reaching process of GDM and achieve a comprehensive evaluation of current consensus methods through an efficiency analysis of consensus costs and consensus improvement. From the perspective of efficiency, we propose a benchmark in consensus reaching by data envelopment analysis without explicit input benchmark models, and then present an objective method for consensus threshold determination in GDM. Finally, we use numerical examples to illustrate the usability of our method.

Large-scale group decision-making (LSGDM) deals with complex decision- making problems which involve a large number of decision makers (DMs). Such a complex scenario leads to uncertain contexts in which DMs elicit their knowledge using linguistic information that can be modelled using different representations. However, current processes for solving LSGDM problems commonly neglect a key concept in many real-world decision-making problems, such as DMs’ regret aversion psychological behavior. Therefore, this paper introduces a novel consensus based linguistic distribution LSGDM (CLDLSGDM) approach based on a statistical inference principle that considers DMs’ regret aversion psychological characteristics using regret theory and which aims at obtaining agreed solutions. Specifically, the CLDLSGDM approach applies the statistical inference principle to the consensual information obtained in the consensus process, in order to derive the weights of DMs and attributes using the consensus matrix and adjusted decision-making matrices to solve the decision-making problem. Afterwards, by using regret theory, the comprehensive perceived utility values of alternatives are derived and their ranking determined. Finally, a performance evaluation of public hospitals in China is given as an example in order to illustrate the implementation of the designed method. The stability and advantages of the designed method are analyzed by a sensitivity and a comparative analysis.

Three-way group decisions provide an efficient method to settle complex and high risk decision-making problems. To obtain reasonable decision results that satisfy different backgrounds and knowledge of decision makers, it is necessary to design a proper consensus reaching process (CRP) for loss functions of decision-theoretic rough sets (DTRSs). Unlike existing researches, this paper not only extends the group relationship among decision makers to the social network, but also considers the externality of social trust network in group decision making. In light of this idea, we design a new CRP with the externality of social network for three-way group decisions. In the CRP, the adjustment of a decision maker who is persuaded by the moderator can influence other decision makers to accordingly adjust evaluations. Thus, by using the linkage externality influence among decision makers, we establish a two-stage mixed 0–1 linear optimization consensus model for the determination of loss functions of DTRSs. Then, based on Bayesian decision procedure, we construct a complete decision procedure for three-way group decisions with social network. Finally, we apply our proposed method to assess desert locust invasion areas and verify its validity.

In group decision-making, a consensus-reaching process (CRP) is critical to minimize conflicts among decision-makers. Non-cooperative behaviors during the CRP may slow the consensus achievement or even lead to consensus failure. Previous research has not thoroughly identified various non-cooperative behaviors nor has it developed distinct management strategies for different CRP stages. This study aims to provide a systematic approach for identifying and addressing non-cooperative behaviors at different CRP stages, employing tailored management for each behavior type. We introduce and apply a concept named ‘comprehensive score’ to facilitate varied responses to non-cooperative behaviors throughout the CRP. A null-norm operator-based self-management weight generation mechanism is proposed to monitor experts’ historical performance, while a systematic analysis of experts’ characteristics enables detailed classification of non-cooperative behaviors. Through the research, we find that there are seven types of non-cooperative researches which needs to be respectively addressed according to its effects. The proposed management scheme improves the efficiency of CRP. Besides, the current research enriches the mechanisms for identifying and handling non-cooperative behaviors. It offers methodological references for non-cooperative behaviors management in more complex decision-making scenarios.

In multi-criteria group decision making (MCGDM), experts from various backgrounds hold asymmetric knowledge structures, which may impact the opinion aggregation of MCGDM. Hence, considering the experts’ different knowledge structures, this paper applies three-way conflict analysis into opinion interaction for consensus reaching process (CRP). More specifically, we first construct a social network of experts based on the asymmetric influence, which can guide the opinion interaction process. Then, with the aid of three-way conflict analysis, three levels are taken into consideration: (1) With respect to the conflicts from the social relationship level, we identify the conflict relation between the experts and the group via three-way conflict analysis. (2) From the perspective of the alternative level, we develop an opinion interaction rule by dividing the alternatives into strong conflict, weak conflict, and no conflict. (3) From the criteria level, we also design a criteria interaction rule based on the similarity and asymmetry of the experts’ knowledge structures. Thirdly, direction rules with the three levels above are proposed for the CRP. Our proposed method with three-way conflict analysis not only resolves conflicts among experts and minimizes information loss during the process of opinion interaction, but also promotes the CRP. Finally, numerical experiments and comparative simulations are conducted to demonstrate the viability and efficacy of our proposed method.

Large-scale group decision-making (LSGDM) based on social networks has become an important part of practical decision-making. The trust relationship in social networks has an influence on not only the clustering process but also the consensus reaching process (CRP). Decision-makers (DMs) can take different behaviors by using the trust relationship to influence consensus reaching, so identifying the adjustment behaviors of DMs in CRP is essential. This study considers the influence of the trust relationship on the CRP and proposes a behavior analysis-based consensus model that comprehensively considers the leadership behaviors and non-cooperative behaviors. First, based on the clustering result, the preference similarity of two DMs with the direct trust relationship is calculated to judge whether leadership behavior exists. By judging the leadership behaviors, the number of effective DMs involved in LSGDM will be reduced. Second, based on the identification of leadership behaviors, the non-cooperative or cooperative behaviors are defined by judging whether the adjustment behaviors of effective DMs are conducive to achieving group consensus. Third, the weights of effective DMs and subgroups are punished or rewarded by quantifying the degree of non-cooperative or cooperative behaviors. Finally, the simulation experiments and comparative analysis are presented to illustrate the efficiency of the proposed method.

Multi-criteria group decision-making (MCGDM) problems, where correlations commonly exist among input arguments, are becoming increasingly complex. However, most of the existing consensus-reaching methods for MCGDM problems fail to adequately consider the effects of these interactions among criteria and experts, which may bring about inaccurate results. Therefore, this paper establishes a novel MCGDM framework based on the generalized Shapley value to solve the consensus-reaching problem with interval-valued Pythagorean fuzzy sets (IVPFS). First, experts’ evaluations are collected using IVPFS, which offers a more flexible way to express this vague information. Second, the interval-valued Pythagorean fuzzy Choquet integral operator and the interval-valued Pythagorean fuzzy Shapley aggregation operator are developed to fuse the decision information with complementary, redundant, or independent characteristics. Third, an integrated consensus-reaching algorithm is established to improve group consensus by iteratively updating the evaluations until the group consensus level reaches the preset threshold. Then, the classical PROMETHEE method is extended using the generalized Shapley value within an IVPFS context to derive a more scientific ranking result. Finally, a case study for a sustainable supplier evaluation problem is presented to validate the proposed method. The results and comparative analysis show that the proposed method can represent experts’ evaluations more flexibly, integrate inputs with interrelationships more effectively, and improve group consensus more efficiently.

In real-world complex group decision-making problems, preference inconsistency and opinion conflict are common and crucial challenges that need to be tackled. To promote consensus reaching, a novel group consensus reaching model is constructed considering individual satisfaction and group fairness. This study focuses on managing the group consensus reaching process based on flexible and adaptable information, modelled as distributed linguistic preference relations (DLPRs). First, a building process for DLPRs is discussed by integrating cumulative distribution functions converted from single linguistic term sets, hesitant fuzzy linguistic term sets, and comparative linguistic expressions. Furthermore, a two-stage consistency improvement method is proposed, which makes a trade-off between the frequency and magnitude of adjustments. Finally, we establish an improved group consensus model to balance individual satisfaction and group fairness, where individual satisfaction is measured by the deviation between the original and revised preferences and group fairness is measured by the deviation between individual satisfactions. The emergency response plan selection is conducted to show the validity and advantages of the proposed approach.

In multi-criteria group decision making (MCGDM) with qualitative settings, hesitant fuzzy linguistic term sets (HFLTSs) provide a flexible way to capture decision makers (DMs)’ hesitancy when eliciting linguistic expressions. However, existing studies overlook the fact that words mean different things to different people, which entails that DMs have personalized individual semantics (PISs) in terms of their expressions in linguistic MCGDM. This study develops a novel framework to address hesitant fuzzy linguistic MCGDM considering PISs of DMs. First, the concept of discrimination measure for DMs is defined. Based on the discrimination measure, a discrimination-based optimization model and a multidimensional preference-based optimization model are established to derive personalized numerical scales (NSs) of linguistic terms for DMs in different situations. Second, a consensus-reaching method based on an optimization model that aims to minimize the amount of adjustments between the original and updated linguistic decision matrices and to preserve their accuracy is constructed to yield a consensual solution. Finally, an illustrative example followed by comparative and sensitivity analysis is presented to demonstrate the application and features of the proposed framework in this study.