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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.

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.

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.

The matching service the lending platform (moderator) provides acts as a facilitative conduit for reaching a loan consensus, facilitating agreements among multiple lenders and borrowers (decision makers). In light of the reality that decision-makers exhibit varying sensitivities to compensation expectations in response to opinion adjustment, the moderator’s demonstration of a preferred compensation mechanism determines the efficiency of the matching service. This article proposes a dynamic cost compensation mechanism driven by moderator preferences for group consensus in lending platforms. Firstly, the utility function describes adjusters’ preferences, defining three unit cost compensation preferences: Power-type I, II and right-partial S-shaped preferences. Subsequently, we construct a generalized dynamic minimum-cost consensus decision model to determine the optimal unit compensation strategies within the opinion interval delineated by the moderator. For the likelihood of equitable concerns arising from fluctuations in unit compensation costs, we enforce the fairness of the compensation strategy by incorporating the Gini coefficient as a constraint within the consensus model. To validate the effectiveness and applicability of the proposed models, we apply the proposed models to online lending utilizing data obtained from an online peer-to-peer lending platform.

As global climate change intensifies and fossil fuel resources continue to deplete, transitioning to alternative energy sources has become a vital strategy for sustainable development. Photovoltaic (PV) power generation, recognized for its clean, renewable, and low-carbon characteristics, is advancing rapidly. Against this background, site selection for PV power plant stations has become a crucial decision-making factor in ensuring project success. However, in large-scale group decision-making (LGDM), the complex backgrounds and substantial number of decision-makers (DMs) pose a significant challenge in reaching consensus efficiently. Therefore, this paper proposes a multi-objective optimization consensus model (MOOCM) utilizing dynamic trust networks to solve LGDM problems. First, a hybrid trust network (HTN) is built by integrating preference similarity and trust relationships, and DMs are clustered using the Louvain algorithm based on this hybrid network. Second, a MOOCM is designed with the objectives of minimizing costs, maximizing fairness, and achieving a high consensus level. Then, after consensus is reached, the HTN is updated, and secondary clustering is performed to obtain dynamic weights for DMs. Finally, a PV power plant site selection problem with 20 DMs, four alternatives, and four attributes is used as a case study for validation. In the first clustering, the DMs are divided into four subgroups. After consensus is reached, the HTN is updated and a second clustering is performed, which finally produces three subgroups. At the same time, the proposed method can achieve a group consensus level (GCL) of 0.9597, with Cost = 1.7422 and Fairness = 0.9043. These results verify the effectiveness and practical utility of the proposed method in LGDM.

Emergency decision-making problem is common in our daily life. To solve this kind of problem, a group of decision-makers (DMs) are usually invited to make a decision in a limited time. Since multiple attributes are usually considered, it’s called large-scale multi-attribute emergency group decision-making (LS-MA-EGDM). There are two issues in the general research of LS-MA-EGDM. First, clustering and consensus-reaching process (CRP) should consider the influence of DMs’ intrinsic features. Second, consensus adjustment within and among sub-clusters ought to be fast to prevent multi-round iteration. Accordingly, (1) we introduce graph attention mechanism to calculate the attention coefficients between DM pair’s intrinsic features. The multi-head graph attention coefficient based on social network analysis (SNA) is proposed, which is then combined with opinion similarity to construct a social network clustering method. (2) The Einstein product operator is introduced to propagate the attention coefficients and yield DMs’ weights, which is then incorporated in the subsequent adjustment allocation. (3) Identification rules are provided based on four consensus types in the CRP. The one-iteration personalized adjustment strategies corresponding to different consensus types are then proposed. (4) Evidential reasoning (ER) algorithm is finally utilized to aggregate the preferences of clusters after consensus is reaching. The proposed method is further applied to a chemical plant explosion in Texas to illustrate its effectiveness and validity in dealing with emergencies.

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.