Large-scale Group Decision-making Problems Research Articles

Dynamic clustering-based consensus model for large-scale group decision-making considering overlapping communities

Consensus-reaching strategy is crucial in large-scale group decision-making (LSGDM) as it serves as an effective approach to reducing group conflicts. Meanwhile, the common social network relationships in large groups can affect information exchange, thereby influencing the consensus-reaching process (CRP) and decision results. Therefore, how to leverage social network information in LSGDM to obtain an agreed solution has received widespread attention. However, most existing research assumes relative independence between communities in the dimension reduction process of LSGDM and neglects the possibility of different overlaps between them. Moreover, the impact of overlapping communities on CRP has not been adequately explored. Besides, the dynamic variations in clusters and their weights caused by evaluation updates need to be further studied. To address these issues, this paper proposes a dynamic clustering-based consensus-reaching method for LSGDM considering the impact of overlapping communities. First, the LINE-based label propagation algorithm is designed to cluster decision makers (DMs) and detect overlapping communities with social network information. An overlapping community-driven feedback mechanism is then developed to enhance group consensus by utilizing the bridging role of overlapping DMs. During CRP, clusters and their weights are dynamically updated with trust evolution due to the evaluation iteration. Finally, a case study using the Film Trust dataset is conducted to verify the effectiveness of the proposed method. Simulation experiments and comparative analysis demonstrate the capability of our method in modeling practical scenarios and addressing LSGDM problems under social network contexts.

Minimum cost consensus model with variable cost for multi-criteria large-scale group decision-making considering the tolerance of decision-makers

The objective of multicriteria large-scale group decision-making (LSGDM) is to obtain a decision result that gains acceptance from the majority of decision-makers (DMs). The consensus reaching process (CRP) plays a crucial role in guiding DMs to continuously adjust their opinions through feedback adjustment mechanisms to form a widely accepted decision result. In practical decision-making, adjusting opinions incurs costs and involves limited resources. Simultaneously, DMs have tolerance for modifying their opinions. To this end, this paper proposes a minimum cost consensus model (MCCM) with variable cost to reach consensus efficiently within limited resources and DMs’ tolerance. Firstly, a method to measure the combined similarity among DMs is proposed. Then, an extended local fitness maximization (ELFM) algorithm suitable for multicriteria LSGDM problems is proposed for clustering. Furthermore, an objective method of determining the unit adjustment costs for DMs in the MCCM is provided. For the CRP that considers the tolerance of DMs, this paper introduces the MCCM with variable cost to obtain the adjustment opinions of DMs. During the selection process, we utilize the stochastic multicriteria acceptability analysis (SMAA) method to evaluate alternatives and selection. Finally, the feasibility of the proposed method is verified through an illustrative example, and its advantages are emphasized through comparative analysis.

A conceptual clustering method for large-scale group decision-making with linguistic truth-valued lattice implication algebra

The increasing complexity of decision-making environments has led to a rise in the involvement of decision-makers (DMs) in group decision-making problems. Clustering is widely used in large-scale group decision-making (LSGDM) to categorize DMs into smaller groups. Ensuring reasonable decision-making results requires providing explanations for the generated groups during the clustering process. To address the clustering problem in LSGDM within uncertain linguistic environments, this paper proposes a conceptual clustering method based on the linguistic concept lattice. The method efficiently manages comparable and incomparable linguistic information. To achieve interpretable clustering results for DMs, attribute and expert induction matrices are first introduced. Cluster stability analysis is then employed to automatically determine the optimal number of clusters. Second, linguistic truth-valued aggregation operators are proposed to aggregate the linguistic evaluation information of DMs in each cluster. In addition, a consensus reaching process is conducted within each cluster, and a feedback mechanism is established to iteratively update clusters when consensus cannot be reached. Finally, numerical examples and comparative analyses are presented that verify the effectiveness of the proposed approach in effectively addressing the LSGDM problem within uncertain linguistic environments.

Prospect theory-based large-scale group decision-making method with heterogeneous preference relations

Large-scale group decision-making (LSGDM) issues are increasingly prevalent in modern society across various domains. The preference information has emerged as a widely adopted approach to tackle LSGDM problems. However, a significant challenge lies in facilitating consensus among decision-makers (DMs) with diverse backgrounds while considering their hesitation and psychological behavior. Consequently, there is a pressing need to establish a novel model that enables DMs to evaluate alternatives with heterogeneous preference relations (HPRs). To this end, this research presents a new consensus-building method to address LSGDM problems with HPRs. First, a novel approach for solving collective priority weight is introduced based on cosine similarity and prospect theory. In particular, a new cosine similarity measure is defined for HPRs. Subsequently, a consensus index is provided to gauge the consensus level among DMs by considering their psychological behavior and risk attitudes. Further, a consensus-reaching model is developed to address LSGDM with HPRs. Finally, an instance of supplier selection is presented to demonstrate the practicality and efficacy of the proposed method.

A consensus model considers managing manipulative and overconfident behaviours in large-scale group decision-making

When dealing with large-scale group decision-making problems, the central emphasis lies in the objective and rational acquisition of a collective opinion acceptable to the majority of decision makers. Manipulative and overconfident behaviours are two common behaviours that make the decision results deviate from the objective facts in the decision-making process. To manage manipulative and overconfident behaviours in decision-making, this paper investigated a novel consensus model based on social networks. A novel efficient clustering model is first proposed in the model, in which the subgroups' combined cohesion is considered. Furthermore, for the manipulative behaviour of decision makers, we proposed an improved method for the identification and management based on trust relationships. In the consensus reaching process, we proposed a new identification mechanism to promote consensus reaching effectively. In the feedback mechanism, the social network DeGroot model is employed to adjust the opinions of decision makers. Moreover, a management approach is proposed for the overconfident behaviour of decision makers in the social network DeGroot model. Lastly, the feasibility and applicability of the proposed model are verified by an illustrative example. Simulation experiments and comparative analysis demonstrate the effectiveness of the model in facilitating consensus reaching.

Conflict management-based consensus reaching process considering conflict relationship clustering in large-scale group decision-making problems

In large-scale group decision-making (LSGDM) events, conflicts among decision makers (DMs) usually occur, causing serious damage to the decision-making process. Accurate conflict detection and timely management in LSGDM can improve the efficiency of the consensus reaching process (CRP) and reduce the overall conflict degree. This paper presents a conflict management-based consensus reaching process (CM-CRP) to achieve centralized and efficient management of DMs. In CM-CRP, to further manage the conflict relationships among DMs, a new clustering algorithm is considered where DMs with conflicting opinions are clustered into a subgroup. To improve the accuracy of the management and precisely the portray behaviors of DMs, for a multi-attributes LSGDM event, the confidence of DMs at the attribute level is captured. Further, the dynamic opinion weight operator is proposed in CM-CRP combining the confidence level and conflict degree of DMs, which enables a more accurate measurement of DMs’ receptivity to others’ opinions. Comparative experiments prove that the proposed CM-CRP outperforms the existing CRP, and several simulations investigate the effect of different factors on the CM-CRP.

A two-stage consensus model for large-scale group decision-making considering dynamic social networks

Clustering and the feedback mechanism in a consensus reaching process (CRP) have been regarded as two critical components when solving the large-scale group decision-making (LSGDM) problem. However, the necessity of treating decision makers (DMs) as a dynamic social network (in terms of their trust relationships) in the DM clustering has not been fully investigated. Also, with people's increased democratic awareness, it appears essential to consider the individual's willingness to cooperate when designing the feedback mechanism in the CRP. This study will focus on solving the LSGDM problem considering dynamic social networks and propose a novel two-stage consensus model. First, a hybrid trust network is built to dynamically represent social relationships among DMs (i.e., the hybrid trust network evolves with the CRP). Spectral clustering algorithm is then used to cluster DMs into more trusted sub-groups, thus improving the efficiency of coordinating DMs. Second, a two-stage feedback mechanism is designed to help DMs reach a consensus in a more human-centric manner. To reach a consensus without seriously violating the willingness of DMs, we strike a balance between maximizing the consensus degree and minimizing the adjustment cost and further develop two nonlinear programming models to provide modification suggestions for sub-groups and individuals, respectively. The originality of the proposed consensus model can be summarized as clustering the dynamic hybrid trust network integrated with balancing the decision-making efficiency against the willingness of DMs to cooperate. The feasibility and effectiveness of the developed model are demonstrated through the detailed application study.

A dynamic trust network and influence measure-based consensus model for large-scale group decision-making with incomplete intuitionistic fuzzy preference relations

The proliferation of network technology has led to the focus on large-scale group decision-making (LSGDM).This study establishes a consensus model by constructing dynamic trust networks to address LSGDM problems in an incomplete intuitionistic fuzzy environment. More specifically, an approach to measuring the influence of decision-makers (DMs) is presented by combining opinion similarity and trust relationships among DMs. Subsequently, an estimation method for missing values in incomplete intuitionistic fuzzy preference relations (IFPRs) is given by considering the reference risk. With these discussions, a dynamic update method of the trust network is proposed to determine the real-time weights of DMs and subgroups. In addition, a two-stage feedback adjustment mechanism for individuals and subgroups is designed. In the end, a numerical example and comparative analysis are provided to illustrate the feasibility and superiority of the proposed method.

Heterogeneous Large-Scale Group Decision Making Using Fuzzy Cluster Analysis and Its Application to Emergency Response Plan Selection

As the number of people involved in a decision-making problem increases, the complexity of the group decision-making (GDM) process increases accordingly. The size of participants and the heterogeneous information have important effects on the consensus reaching process in GDM. To deal with these two issues, traditional methods divide large groups into smaller ones to reduce the scale of GDM and translate heterogeneous information into a uniform format to handle the heterogeneity problem. These methods face two challenges: 1) how to determine the appropriate group size? and 2) how to avoid or reduce loss of information during the transformation process? To address these two challenges, this article uses fuzzy cluster analysis to integrate heterogeneous information for large-scale GDM problems. First, a large group is divided into smaller ones using fuzzy cluster analysis and the F-statistic is applied to determine the satisfactory number of clusters. The original information is retained based on the similarity degree. Then, a consensus reaching process is conducted within these small groups to form a unified opinion. A feedback mechanism is developed to adjust the small GDM matrix when any group cannot reach a consensus, and the heterogeneous technique for order preference by similarity to an ideal solution (TOPSIS) is used to select the best alternative. To validate the proposed approach, an experiment study is conducted using a practical example of selecting the best rescue plan in an emergency situation. The result shows that the proposed approach helps to choose the best rescue plan faster.

A novel method to estimate incomplete PLTS information based on knowledge-match degree with reliability and its application in LSGDM problem

In recent years, large-scale group decision making (LSGDM) has been researched in various fields. Probabilistic linguistic term set (PLTS) is an useful tool to describe evaluation information of experts when solving the LSGDM problem. As decision-making becomes more complex, in most cases, decision makers are unable to give complete evaluations over alternatives, which leads to the lack of evaluation information. To estimate missing information, this paper proposes a new method based on knowledge-match degree with reliability that knowledge-match degree means the matching level between evaluation values provided by individual and ones from group. The possession of reliability associated with evaluation information depends on fuzzy entropy of PLTS. Compared with previous methods, this approach can enhance accuracy and reliability of estimated values of missing evaluation information. Based on this method, we develop a complete decision process of LSGDM including information collection, subgroup detecting, consensus reaching process (CRP), information aggregation and ranking alternatives. Subsequently, a case about pharmaceutical manufacturer selection is used to illustrate the proposed decision method. To verify effectiveness and superiority, we make a comparative analysis with other methods and finally draw a conclusion.

A clustering- and maximum consensus-based model for social network large-scale group decision making with linguistic distribution

Nowadays, with the increasing complexity of decision-making environment, more and more large-scale group decision making (LGDM) problems are faced. Due to the existence of social network relationships among experts, social network analysis (SNA) is proved to be an effective analysis method for LGDM problems. Meanwhile, it is crucial for LGDM issues to determine the weights of decision groups and to lessen the large-scale DMs’ dimension, which will affect the result of decision making directly. This study proposes a clustering- and maximum consensus-based resolution framework with linguistic distribution (LD) for social network large-scale group decision making (SNLGDM) problems. In the consensus framework, independent sub-groups can be obtained by the division of large-scale DMs according to trust relationship using the proposed SNA-based trust network clustering model, and the LD assessments are used to represent the preference relation of sub-groups. Following this, by considering three dependable sources: consistency, similarity, and in-centrality degree, this paper devises a maximum consensus-based method, which can generate the sub-groups’ comprehensive weight by maximizing the level of consensus between sub-groups and the collective matrix. Meanwhile, the final ranking of alternatives can be obtained based on collective preference relation. Conclusively, the availability and advantage of this research are verified through numerical example, coefficient analysis and comparative analysis.

An Influence Network-Based Consensus Model for Large-Scale Group Decision Making with Linguistic Information

The vast majority of the existing social network-based group decision-making models require extra information such as trust/distrust, influence and so on. However, in practical decision-making process, it is difficult to get additional information apart from opinions of decision makers. For large-scale group decision making (LSGDM) problem in which decision makers articulate their preferences in the form of comparative linguistic expressions, this paper proposes a consensus model based on an influence network which is inferred directly from preference information. First, a modified agglomerative hierarchical clustering algorithm is developed to detect subgroups in LSGDM problem with flexible linguistic information. Meanwhile, a measure method of group consensus level is proposed and the optimal clustering level can be determined. Second, according to the preference information of group members, influence network is constructed by determining intra-cluster and inter-cluster influence relationships. Third, a two-stage feedback mechanism guided by influence network is established for the consensus reaching process, which adopts cluster adjustment strategy and individual adjustment strategy depending on the different levels of group consensus. The proposed mechanism can not only effectively improve the efficiency of consensus reaching of LSGDM, but also take individual preference adjustment into account. Finally, the feasibility and effectiveness of the proposed method are verified by the case of intelligent environmental protection project location decision.

A Large‐Scale Group Decision‐Making Consensus Model considering the Experts’ Adjustment Willingness Based on the Interactive Weights’ Determination

This study proposes a large‐scale group decision‐making (LSGDM) consensus model considering the experts’ adjustment willingness based on the interactive weights’ determination, which can be applied to an LSGDM problem through a case of earthquake shelters. The main contributions of our research are of three aspects as follows. First, the determination method of the interactive weight, which obtains the DMs’ attitude towards the decision‐making results, is presented. The subgroups’ weights are calculated, and the unit adjustment cost for each DM is defined. Second, we introduce an objective consensus threshold by the mean and variance of the consensus level for each subgroup. Subsequently, an identification rule is performed to determine the DM to be adjusted with the large difference and the low adjustment cost. And we developed a novel consensus adjustment method that takes the DMs’ adjustment willingness into account to retain as much original information as possible. Thirdly, in order to reduce the subjectivity of the preset consensus threshold and the maximum number of iterations, an objective consensus termination condition that combines the current group consensus level and the consensus adjustment rate is put forward. Finally, the proposed model has demonstrated its effectiveness and superiority based on the comparative and sensitive analysis through a practical example.

Information consistent degree‐based clustering method for large‐scale group decision‐making with linear uncertainty distributions information

Clustering analysis is a key technique in reducing the dimensionality of high volume irregular data containing large-scale group decision-making (LSGDM) information. Uncertainty theory is suitable for subjective estimation or situation, such as lack of historical data, and it can be employed to effectively express the uncertainty of trust and preference information in LSGDM problems. This paper studies the dimensionality reduction and subgroup optimization in LSGDM by utilizing linear uncertain variables in social networks. A clustering method is proposed to decompose the large group into several subgroups of higher consilience degrees and higher preference similarities, and lower the dimension of information for LSGDM. In the clustering process, two measurement attributes, trust relationship and preference relationship of decision-makers, are combined, and information consistent degree is utilized as the clustering indicator. This approach does not need to preset the threshold and the number of subgroups, and can be employed to obtain subgroups with similar preferences and stable trust relationship. Through the clustering reliability evaluation of subgroups, the rationality of large-scale group clustering results is verified. Subgroup consensus contribution is used to identify superior subgroups and quantify the role of subgroups in improving the consensus level. An example of emergency decision-making and comparative analysis is provided to explain the feasibility and advantages of the proposed method.

How to process local and global consensus? A large-scale group decision making model based on social network analysis with probabilistic linguistic information

With the rapid development of societal and technological paradigms, large-scale group decision making becomes an emerging topic. In conventional group decision making methods, it is often assumed that all experts are independent. However, with the expansion of social media, experts usually have some relationships and get together for some reasons such as the academic relationship, working relationship or common interests. In these cases, experts are no longer independent individuals. To address the issue, this study introduces a large-scale group decision making model based on the social network analysis. In this model, experts can provide trust values on other experts. Due to the scale and complexity of the large-scale group decision making problems, the dimensional reduction, which uses community detection to classify experts into local communities, is deemed essential. Based on this process, the whole group can be divided into two layers. The first layer is the global network containing all communities, and the second layer is the local network within a community. This study develops a model to address large-scale group decision-making problems considering the local and global consensus in two layers simultaneously. This model allows experts to use probabilistic linguistic preference relations to express their cognitive complex evaluation information. An illustrative example is presented to show the usefulness of the proposed model.

Consensus-Based Linguistic Distribution Large-Scale Group Decision Making Using Statistical Inference and Regret Theory.

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.

Dynamic programming algorithm-based picture fuzzy clustering approach and its application to the large-scale group decision-making problem

Due to the rapid development of society and economy, the large-scale group decision making (LSGDM) problems are increasingly common in the real life. In this paper, a dynamic programming algorithm-based picture fuzzy clustering approach is proposed to solve the LSGDM problems. First, aimed at the limitations of the existing operation laws of picture fuzzy sets, we define some new picture fuzzy operation laws. Based on these operation laws, a new picture fuzzy weighted geometric operator is developed to aggregate the preference information provided by the decision makers. Second, a new picture fuzzy Dice similarity measure is proposed to detect the different correlations between the decision makers. Then, inspired by the dynamic programming algorithm, a new clustering approach is proposed to improve the efficiency and quality of the decision-making. After the clustering process, the picture fuzzy score function is employed to compare and rank the alternatives. Finally, an illustrative example and a comparative analysis are provided to demonstrate the effectiveness and superiority of the proposed method.

Managing manipulative and non-cooperative behaviors in large scale group decision making based on a WeChat-like interaction network

The main challenges in large scale group decision making (LSGDM) problem are how to tackle with the great number of participants and how to achieve a common solution accepted by most of group members. In LSGDM problems, some decision makers (DMs) will exhibit manipulative and non-cooperative behaviors owing to the different interests they might present. Dealing with such large group implies a need for mechanisms to detect DMs’ manipulative and non-cooperative behaviors, which might affect the overall efficiency of the consensus reaching process. This paper introduces a novel framework based on WeChat-like interaction network to analyze manipulative and non-cooperative behaviors in the LSGDM problems. In the developed framework, we first detect and manage the manipulative behaviors based on the interaction network. Afterwards, for the consensus model based on opinion evolution, we develop an approach to identify and manage non-cooperative behaviors under the WeChat-like interaction network context. As a result, both the DMs’ weights and trust network derived from it are dynamically updated in parallel. Detailed simulation experiments and comparison analysis under different input parameters are presented to demonstrate the efficiency of this novel approach for coping with manipulative and non-cooperative behaviors.

Distance-Based Large-Scale Group Decision-Making Method with Group Influence

Large-scale group decision making (LSGDM), which involves a large number of decision makers, has become a hot topic in the field of decision making. To address LSGDM problems with hesitant information, in this paper, a distance-based LSGDM method is proposed by considering group influence. In the method, a generalized distance measure between two pieces of hesitant information is designed to overcome the limitations of existing distance measures. To accelerate the convergence of consensus reaching process with the consideration of the interaction among decision makers, decision makers are divided into several subgroups. The group leader is selected in terms of the contributions of decision makers to group consensus. In order to help generate a satisfactory solution by adequately considering the decision makers’ diverse opinions, the group discussion is introduced to clarify their opinions and minimize bias under the organization of the selected group leader. Based on the changes in the preference information before and after group discussion, the influence of each subgroup is generated and further applied to determine the weights of subgroups. Simulation and comparison experiments are conducted to demonstrate the applicability and effectiveness of the proposed method.

Comprehensive minimum cost models for large scale group decision making with consistent fuzzy preference relations

Nowadays, society demands group decision making (GDM) problems that require the participation of a large number of experts, so-called large scale group decision making (LS-GDM) problems. Logically, the more experts are involved in the decision making process, the more common is the emergence of disagreements in the group. For this reason, consensus reaching processes (CRPs) are key in the resolution of these problems in order to smooth such disagreements in the group and reach consensual solutions. A CRP requires that experts are receptive to change their initial preferences, but demanding excessive changes could lead to deadlocks. The well-known minimum cost consensus (MCC) model allows to obtain an agreed solution by preserving experts’ preferences as much as possible. However, this MCC model only considers the distance among experts and collective opinion, which is not enough to guarantee a desired degree of consensus. To overcome this limitation, it was proposed comprehensive MCC models (CMCC) in which both consensus degree and distance are considered, and CMCC models deal with fuzzy preference relations (FPRs) for modeling experts’ opinions. However, these models are not efficient to deal with LS-GDM problems and the FPRs consistency is ignored in them. Therefore, this paper aims to propose new CMCC models focused on LS-GDM problems in which experts use FPRs whose consistency is taken into account in order to obtain reliable results. A case study is introduced to show the effectiveness of the proposed models.