Group Consensus Level Research Articles

A minimum cost and maximum fairness-driven multi-objective optimization consensus model for large-scale group decision-making

The rise of social media and e-democracy has driven a paradigm shift in decision-making, notably reflected in the changing ways of public participation and policymaking within decision-making processes. The increased focus on fairness and efficiency not only complicates the consensus-building process among diverse interests and perspectives, but also significantly adds to the complexity of decision-making and its implementation. In this context, balancing the interests of all parties while ensuring fairness and improving decision-making effectiveness becomes crucial. To address these challenges, this study develops a multi-objective optimization consensus framework for large-scale group decision-making (LSGDM) that integrates the interests of decision-makers (DMs) and a moderator, providing a more comprehensive tool. Specifically, this study first designs a DM weight determination method based on structural hole theory within fuzzy social networks. The proposed DM weight determination method effectively leverages the flexibility of fuzzy social networks and the comprehensiveness of structural hole theory to enhance the accuracy and reliability of weight assignment. Building on this, a novel clustering method based on the maximum group consensus level is developed, taking into account the varying importance of different DMs. Furthermore, a minimum cost and maximum fairness-driven multi-objective optimization LSGDM consensus model, referred to as MCMF-MO-LSGDM, is explored in this study. Finally, the utility and superiority of the constructed model are confirmed through comparative analysis and simulation experiments against existing related works.

A dual-level consensus model for large-scale group decision-making driven by trust relationships in social networks

In large-scale group decision-making, obtaining reasonable and reliable decision results is the research focus. To this end, a dual-level consensus model for large-scale group decision-making is constructed. In the model, we first presented a method for measuring the two-dimensional similarity between decision-makers. The method considered the opinion similarity at evaluation scales and ranking results level, which provided a more comprehensive measure of the opinion differences between decision-makers. A hierarchical clustering algorithm based on the two-dimensional similarity-trust matrix is proposed. By considering the two-dimensional similarity and trust relationships among decision-makers, the method contributed to the formation of subgroups with excellent cooperative and communicative atmospheres. Furthermore, we introduced a dual-level consensus measures method to comprehensively and accurately assess the group consensus level. To increase the efficiency of decision-making and the satisfaction of decision-makers, we proposed a personalized feedback adjustment mechanism for decision-makers. Additionally, for the subgroups that have not reached consensus, a social networks DeGroot model is constructed to adjust the opinion of subgroups. Finally, a case study of low-carbon supplier selection verified the feasibility and applicability of the model. The effectiveness and superiority of the model are demonstrated by comparative and simulation analysis. The analysis results show that the model is conducive to promoting cooperation and coordination among decision-makers and obtaining highly acceptable and quality decision results.

Interactive dynamic trust network for consensus reaching in social network analysis based large-scale decision making

With the advances in social media and e-democracy technologies, large-scale decision making (LSDM) problems with trust relationships demands effective consensus-reaching processes. Existing literature has identified a need for improvement in the updating method of trust relationships and the recommendation-feedback mechanism, while the overall effect of trust relationships on consensus reaching remains unexplored and not quantitatively examined. This study proposes a novel interactive dynamic trust-lead consensus reaching process (IDT-CRP) based model to address these challenges. The model integrates a dynamic Trust network updating (DTNU) process and a trust-lead and efficiency-driven recommendation-feedback (TERF) process. In the DTNU process, secondary trust is defined to represent the trust derived from decision makers’ modification behaviors in each iteration. In the TERF process, a novel trust-lead and efficiency-driven recommendation-feedback mechanism is proposed, in which two different decision scenarios are provided. Furthermore, the role of trust relationships in enhancing group consensus level is analyzed, revealing its significant impact while identifying an upper limit. Novelties of this paper include 1) the improved trust updating algorithm which derived secondary trust from modification behaviors instead of opinion similarities; 2) the improved recommendation-feedback mechanism with different trust utilization scenarios while retaining minority opinions; 3) the novel IDT-CRP model based on the interactive mechanism between trust relationship and opinion evolution. A series of experiments are implemented, validating that the proposed model is of good feasibility, effectiveness and robustness, and can be applied in future LSDM research.

An Incentive Mechanism-Based Minimum Adjustment Consensus Model Under Dynamic Trust Relationship.

In traditional group decision making, the inconsistent experts are usually forced to make compromises toward the group opinion to increase the group consensus level. However, the strategy of reaching group consensus via an incentive mechanism encouraging adjustment of preferences is more effective than forcing, which is the aim of this article. Specifically, this article establishes a novel incentive mechanism to support group consensus under dynamic trust relationship. First, the supremum and infimum incentives-based rule driven by trust relationship is defined. Based on the assumption that if incentive conditions are met, then experts will be willing to adjust their preferences, the incentive behavior-driven minimum adjustment consensus model is developed to generate optimal incentive-based recommendation preferences. Thus, the proposed incentive mechanism can effectively reduce the preference adjustment cost and promote group consensus reaching. Third, the updated trust relationships between experts are shown to be strengthen by the proposed incentive-driven preference revision. Consequently, the optimization model based on trust interaction relationship is constructed to obtain the final group preference matrix. Finally, a supplier selection case of high-end medical equipment is provided to illustrate the proposed method and show the rationality and advantages of the proposed methodology with both a sensitivity analysis and a comparison analysis.

A group decision-making method for technology selection of petrochemical enterprises

Selecting appropriate energy conservation and emission reduction technologies is essential for the sustainable developments of petrochemical enterprises. It usually involves experienced experts from multi-domain and thus can be regarded as a large-scale group decision-making problem. Existing methods assumed that different experts use the same linguistic term set following the same semantics to express their evaluation values, and derived the ranking of alternatives by an indirectly obtained group preference matrix. Such an approach may induce information loss. To avoid these defects, this study introduces a model based on rank centrality and expert differences to choose appropriate technologies for petrochemical enterprises. First, an attitude parameter is introduced into a linguistic scale function to unify different judgment benchmarks of experts regarding the same linguistic term. Next, a direct weight elicitation method based on rank centrality is developed to deduce the individual rank vector of alternatives. A grey clustering method based on the similarities of individual rank vectors is extended to cluster experts into small groups, and the silhouette coefficient is used to determine clusters weights. Afterwards, the rank vectors of alternatives corresponding to subgroups and the global rank vector are calculated by the weighted averaging operator. Alternatives are ranked by the rank vector of the global group. Finally, four technologies were evaluated by the model, and the preferred technology was identified. The findings indicate that the proposed technology selection model alleviates information loss, elevates group consensus level, and provides a perspective for petrochemical enterprises in search of energy conservation and emission reduction technologies.

An adaptive consensus model for multi-criteria sorting under linguistic distribution group decision making considering decision-makers’ attitudes

Group multiple criteria sorting (MCS) has become a trend in dealing with a variety of practical problems. During the process of managing group MCS, it is critical to reduce conflicts among decision-makers (DMs). Given the key role of DMs’ attitudes in affecting consensus level, this study aims to propose a novel consensus-based approach to solve group MCS problems considering DMs’ attitudes with flexible expression linguistic distribution assessments (LDAs) that can capture massive DMs’ qualitative preferences. To achieve this goal, first, a minimum adjustment-based optimization model is built to guide individuals in revising their preferences, and a maximum assignment interval-based optimization model is constructed to derive consistent and possible assignments of each alternative while maintaining the accuracy levels of the original assignments. An attitudinal consensus index is then defined to measure the group consensus level, by which group DMs’ attitudes can be well considered in MCS problems. A sophisticated adaptive feedback adjustment mechanism is also developed and inserted into the consensus model, which provides support for consensus-reaching based on the advantages of both types of adaptive feedback adjustment mechanism strategies. Afterwards, to generate more straightforward and scientific assignment solutions, this study proposes a minimum information loss-based optimization model to identify the final categories of each alternative. Finally, an illustrative example for evaluating livable cities, followed by sensitivity and comparative analyses, is presented to demonstrate the applicability and advantages of the proposed MCS approach.

New distance measure-driven flexible linguistic consensus model with application to urban flooding risk assessment

As a novel linguistic representation tool, flexible linguistic expression (FLE) has substantial flexibility in expressing ambiguous and uncertain information from experts. However, FLEs pose the following challenges to developing information measurement and consensus mechanisms for FLEs-based multi-attribute group decision-making (MAGDM). (1) The current studies primarily use linguistic distribution approximation or triangular fuzzy numbers to measure the difference between FLEs indirectly without proposing an exact distance measure. (2) Few studies have been conducted on direct accurate consensus models incorporating adaptive consensus feedback mechanisms. To deal with these issues, the flexible linguistic ordinal Deng entropy (FLODE) is firstly proposed to measure the uncertainty of FLEs, and by combining it with linguistic scale functions, a new distance measure for FLEs is constructed, which can accurately measure the level of group consensus and the difference in pairwise FLEs. Subsequently, by integrating the defined FLODE with the classical entropy weight method, a new method for determining the experts’ personalized attribute weights is constructed, fully considering the impact of experts’ personalized attribute weights on decision-making results. Also, a new consensus model incorporating a minimum adjustment feedback mechanism and dynamic personalized attribute weights is developed, in which the feedback adjustment coefficients and personalized attribute weights are dynamically updated during the consensus reaching process (CRP). Lastly, an urban flooding risk assessment is applied to confirm the effectiveness of the proposed consensus model.

A similarity-conformity-based clustering and decentralized feedback mechanism to manage incompatible decision-makers in large-scale group decision-making

This study proposes a similarity-conformity-based clustering and decentralized feedback mechanism to manage incompatible decision-makers (DMs) in the large-scale group construction decision-making problem. Firstly, conformity is proposed to measure the consistency of the most preferred alternative of any two DMs and then extends this concept to define the similarity-conformity level of DMs. The average conformity between DMs in a subgroup represents the cohesion degree of this subgroup. Based on these concepts, a new clustering method considers the conflicts of interest among DMs and introduces the similarity-conformity to divide them into several subgroups. Then, the number of DMs in a subgroup and the cohesion degree are combined to formulate the subgroups’ weights. A decentralized feedback mechanism is proposed to manage two categories of incompatible DMs in the consensus-reaching process. The proposed consensus model adjusts the incompatible DMs’ opinions or subgroups’ weights under four scenarios. In the proposed model, the four adjustment methods prove to be convergent, and they improve the group consensus level by ensuring the DMs’ conformity and the logical consistency of preference relation. Finally, it provides an example of the alternative selection for transportation infrastructure construction. The comparative study and the sensitivity analysis are performed to verify the effectiveness of the proposed method.

Group efficiency and individual fairness tradeoff in making wise decisions

In group decision making, the consensus model with minimum cost has been researched with the aim of improving group efficiency and saving resources. However, one limitation of the minimum cost consensus model is that the reach of consensus is usually at the expense of some group members. We consider two issues that we see as keys in group consensus: efficiency and fairness. We propose the price of fairness in the opinion revision process and give two kinds of fairness schemes. According to the individual's perception of inequity, we introduce inequity aversion parameters and classify experts into two types: experts with non-cooperative behaviors and with altruistic behaviors. Experts with altruistic behaviors will be allowed to contribute more than the recommended number of modifications. Then, we discuss how to achieve the tradeoff between efficiency and fairness. Furthermore, with the rapid development of social media, cloud, and e-government platforms, collective intelligence (CI), i.e., groups of individuals doing things collectively that seem intelligent, has been a hot topic. We expand our work to a crowd context with many individuals. We investigate how the opinion revision process and fairness schemes can influence the emergence of CI. Results suggest that the proportional fairness and max-min fairness have similar performance in stimulating CI. Moreover, the improvement of group accuracy is mainly related to two factors: the group consensus level of initial opinions and the relative distance between group aggregated opinion and the ground truth.

Dual consistency-driven group decision making method based on fuzzy preference relation

Consistency testing and adjustment of preference relations are prerequisites for group decision making; the forced integration of preference relations without consensus may lead to misleading decisions. To address this issue, following the principle of minimal information loss in consensus reaching, we propose a dual consistency-driven group decision making method based on the fuzzy preference relation between individuals and groups. First, a bidirectional adjustment amount is introduced in the individual consistency process to avoid unidirectional expansion or reduction of the degree of fuzzy preference. Second, considering that the adjustment of fuzzy preference information in the process of group negotiation will change the weight of expert, a goal programming based on the dual adjustment of dynamic weights and preference information is constructed, which can solve the problem of contradictory order values before and after the expert weights adjustment and improve the level of group consensus and the efficiency of group consensus reaching. Finally, the effectiveness of the proposed methodology through an analysis of case studies is verified.

Group decision making based on relative projection between fuzzy preference relations

Group decision making (GDM) has been widely focused on for coping with the complexity of a practical decision making problem. This paper proposes a relative projection-driven GDM model with fuzzy preference relations (FPRs). First, a novel additive consistency index of FPRs is constructed using the variance of relative projections between column/row vectors in two FPRs, which is called the relative projection variance consistency index (RPVCI). The thresholds of RPVCI for FPRs with acceptable additive consistency (AAC) are calculated using the simulation method. For improving consistency of FPRs, a convergent iteration algorithm is constructed by equipping subjective and objective adjustment parameters. Second, the group consensus level is captured using relative projections of individual FPRs on the collective one. An iteration model is reported to optimize the consensus degree by combining the weights of experts with a comprehensive adjustment coefficient that depends on both subjective and objective factors. Third, a novel GDM algorithm is proposed by integrating the two proposed iteration models. Comparisons with some existing models are offered by carrying out a case study to show the novelty and advantage of the proposed GDM model.

Limited budget-based consensus model for large group decision making with hesitant fuzzy linguistic information

Considering the uncertainty of large group decision-making and the limitation of resources, this paper constructs a large group decision-making method with hesitant fuzzy linguistic term set (HFLTS) based on limited budget. Firstly, by studying the basic theory of HFLTS, a weighted aggregation model of HFLTS is proposed, which can ensure the minimum weighted distance between aggregated HFLTS and HFLTSs before aggregation. Secondly, a decision makers’ weight determination algorithm is proposed by considering the quality of trust sources in the social trust network, which is calculated by the LeaderRank centrality measure. Furthermore, a maximum group consensus level model (MGCM) based on limited budget is constructed, in which the adjustment cost of decision makers is determined by the hesitancy degree in the evaluation and trust out-degree. For the situation of insufficient budget, the order correlation between the alternatives’ ranking before and after the budget increase is introduced to judge whether to increase the budget to achieve a higher group consensus level. Then, a limited budget-based large group decision-making method with hesitant fuzzy linguistic information is proposed. And this method is applied to the selection of equipment suppliers for hydrogen refueling station. Finally, the effectiveness of the proposed method is verified by comparison with existing research methods and sensitivity analysis.

Linguistic Single-Valued Neutrosophic Multi-Criteria Group Decision Making Based on Personalized Individual Semantics and Consensus

In practical linguistic multi-criteria group decision-making (MCGDM) problems, words may indicate different meanings for various decision makers (DMs), and a high level of group consensus indicates that most of the group members are satisfied with the final solution. This study aims at developing a novel framework that considers the personalized individual semantics (PISs) and group consensus of DMs to tackle linguistic single-valued neutrosophic MCGDM problems. First, a novel discrimination measure for linguistic single-valued neutrosophic numbers (LSVNNs) is proposed, based on which a discrimination-based optimization model is built to assign personalized numerical scales (PNSs). Second, an extended consensus-based optimization model is constructed to identify the weights of DMs considering the group consensus. Then, the overall evaluations of all the alternatives are obtained based on the LSVNN aggregation operator to identify the ranking of alternatives. Finally, the results of the illustrative example, sensitivity and comparative analysis are presented to verify the feasibility and effectiveness of the proposed method.

Mining Personalized Individual Semantics of Self-confidence Participants in Linguistic Group Decision-Making

Words representing individual preferences in group decision-making (GDM) are always associated with different meanings. Consequently, mining personalized semantics of decision-makers (DMs) hidden in preference expressions, and establishing a corresponding management mechanism, is an effective way to reach group consensus through computing with word methodology. However, the aforementioned consensus-reaching process may be hindered by self-confidence. To address this limitation, this study proposes a linguistic group decision model with self-confidence behavior. First, we identified the corresponding self-confidence levels for each DM. Next, we integrated different linguistic representation models into unified linguistic distribution-based models. We then obtained individual personalized semantics based on a consistency-driven optimization method, and designed a feedback-adjustment mechanism to improve the adjustment willingness of DMs and group consensus level. Finally, we conducted a quantitative experiment to demonstrate our model’s effectiveness and feasibility.

Consensus Reaching in Multiple Attribute Group Decision Making: A Multi-Stage Optimization Feedback Mechanism With Individual Bounded Confidences

Existing consensus models focus on improving the group consensus level, but ignore whether a higher group consensus level means higher mutual acceptance of decision makers. In the field of opinion dynamics, the bounded confidence model asserts that the decision makers will accept the preferences of others within a neighborhood of theirs with width a certain confidence level. Inspired by this research methodology, this article develops a consensus model to address the acceptance issue based on individual bounded confidences. Specifically, a bounded confidence-based consensus measure is designed to measure the level of group mutual acceptance, and a multi-stage optimization feedback mechanism based on individual bounded confidences is proposed to maximize the group mutual acceptance and minimize the amount of preference adjustment. A numerical example and a simulation analysis are included to illustrate the use of the model and to justify its effectiveness, respectively.

Group decision making based on multiplicative consistency and consensus of Pythagorean fuzzy preference relations

Pythagorean fuzzy sets (PFSs) become a useful tool to describe the complex cognition of decision makers (DMs). In this paper, Pythagorean fuzzy preference relations (PFPRs) whose elements are PFSs are used for group decision making (GDM). First, a novel multiplicative consistency of PFPRs is proposed. Then, a programming model is constructed to derive the priority weight vector of PFPRs. Then, an inconsistency-repairing method of PFPRs is designed. Moreover, a group consensus index to calculate the degrees of similarity among PFPRs is proposed and an iterative consensus reaching procedure with PFPRs is developed. By maximizing the group consensus level of PFPRs, a model is built to determine DMs’ weights. Furthermore, a new GDM method based on PFPRs is proposed. Finally, we offer an example to illustrate the proposed GDM method and complete a comparative analysis. The proposed GDM method outperforms the existing GDM methods for GDM in Pythagorean fuzzy environments.

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.

A Fuzzy-Social Network Multi-criteria Group Decision-Making Framework for Selection of Renewable Energy Project: A Case of China

The proper selection of a renewable energy project (REP) is the key to give play to regional resource advantages and optimize the energy consumption structure. As a complex multi-criteria group decision-making (MCGDM) problem, the choice of REP involves many influencing factors such as economy, society, and environment. To solve this problem, this paper proposes a social network MCGDM framework based on social network analysis (SNA) and hesitant probabilistic fuzzy set (HPFS). Firstly, the HPFS is introduced into the social network and constructs the hesitant probabilistic fuzzy trust function to represent the trust relationship between decision-makers. Secondly, the trust propagation operator of the hesitant probabilistic fuzzy trust function is constructed using the idea of conditional probability; then a dual feedback mechanism including opinion modification and weight adjustment is proposed to improve the group consensus level. On this basis, a social network MCGDM framework for REP selection is further proposed, and the SNA method is applied to the selection of REP for the first time. Following this, a case in Zhejiang Province, China, is presented to prove the rationality and effectiveness of the framework. The results show that the proposed hesitant probabilistic fuzzy trust function can better reflect the trust relationship between decision-makers and better describe the process of trust transmission, which is of great significance for solving the MCGDM problems such as REP selection.

A novel stochastic group decision-making framework with dual hesitant fuzzy soft set for resilient supplier selection

Suppliers can be regarded as unavoidable sources of external risks in modern supply chains, which may cause disruption of supply chains. A resilient supplier usually has a high adaptive ability to reduce the vulnerability against disruptions and recover from disruption to keep continuity in operations. This paper develops an effective multi-attribute group decision-making (MAGDM) framework for resilient supplier selection. Because of the many uncertainties in resilient supplier selection, the dual hesitant fuzzy soft sets (DHFSSs), a very flexible tool to express uncertain and complex information of decision-makers, is utilized to cope with it. In order to obtain the resilient supplier’s partial order relationship and consider the psychological behavior of decision-makers, this paper proposes the MAGDM framework with DHFSSs based on the TOPSIS method and prospect theory for resilient supplier selection. Furthermore, we consider the consensus level among experts of different backgrounds and experiences and propose a consensus measure method based dual hesitant fuzzy soft numbers (DHFSNs) before selecting a resilient supplier. The expert weights are calculated by the group consensus level between the expert and the group opinions. Meanwhile, we define the entropy of DHFSSs to determine the attribute weights objectively in the decision-making process. Based on this, the proposed method is applied to a practical manufacturing enterprise with an international supply chain for a resilient supplier selection problem. Finally, by performing a sensitivity analysis and a comparative analysis, the results demonstrate the robustness and validity of the proposed method.