Minimum Cost Consensus Model Research Articles

A data-driven minimum cost consensus model for group decision making with personality traits prediction

The minimum cost consensus model (MCCM) proposes an effective method for reaching group consensus in group decision-making problems. Conventional MCCM and its advanced models focus on the different behaviors and psychologies of decision-makers, but, it ignores the heterogeneity of decision-makers that activated them. Therefore, they need to assume the compromise limits and unit adjustment costs of decision-makers, which may be difficult to achieve in practice. To resolve this problem, this study will propose a novel data-driven minimum cost consensus model of different compromise limits and unit costs based on online Big Five personality traits prediction. First, this study uses the Convolutional Neural Network (CNN) and Bi-directional Long-Short Term Memory model (BiLSTM) to obtain the decision-maker's probability of agreeableness based on their Weibo online reviews. Second, a novel minimum cost consensus model considering the decision-maker's personality traits (MCCM-P) is established. To do that, the unit adjustment cost and the personalized compromise limits of decision-makers and their interrelations are defined based on the personality traits prediction. Finally, the MCCM-P is applied in a real group decision-making case study of a university student club activity selection. The result and comparative analysis show that the proposed MCCM model can obtain lower consensus reaching costs than the traditional method.

Minimum adjustment cost consensus model with bounded risk preference attitudes: A perspective based on fractional stochastic dominance

Linguistic multi-attribute group decision making with linguistic distribution assessment (LMAGDM-LDA) problems have been widely investigated. However, in the existing studies, the risk attitudes of decision maker are seldom considered. Inspired by this, in this paper, we employ the idea of fractional stochastic dominance to develop a consensus reaching framework for LMAGDM-LDA with bounded risk preference attitudes. Then, we design an interactive learning algorithm for obtaining the bounded risk preference threshold. Next, we analyze the deception behaviors and average behaviors of experts, and develop the minimum adjustment cost consensus model with bounded risk preference attitude (MACC-BRP). And we justify the connection between the MACC-BRP and the minimum adjustment cost consensus model with other risk attitudes. Furthermore, we provide a distance-based method to obtain the rankings of alternatives. Furthermore, a numerical analysis is provided to show the computation process of the proposed method, and a comparison analysis and a simulation analysis are further conducted to show the advantages and features of the proposal. The simulation results show the effects of the risk preference threshold, the intrinsic individual weight and the average threshold. The comparison results show that the proposed minimum adjustment cost consensus models have clear advantages.

Enhanced minimum cost consensus model for interval type-2 fuzzy social network group decision making focusing on individual attributes and group attitude

In group decision-making scenarios, consensus reaching is a crucial factor for resolving conflicts of opinion among groups, and social network analysis plays a significant role in fostering group consensus. This paper constructs a social network-driven minimum cost consensus framework for interval type-2 fuzzy group decision-making problems involving different individual attributes. Firstly, this paper proposes a theoretical social network analysis by the implementation of propagation efficiency, propagation reliability and opinion similarity to generate comprehensive trust relationships. The aim is to obtain missing trust relationships and individual centrality. Secondly, a minimum cost consensus model is constructed to give recommendation advice for identified inconsistent decision-makers according to their adjustment willingness. The novelty of the model lies in its capability to consider decision-makers’ individual attributes and group attitude or behavior. Then, this paper proposes an interval type-2 fuzzy Alternative by Alternative Comparison (ABAC) method for ranking multiple alternatives which address the rank reversal problem. Lastly, a case study on the selection of alternative charging point operators illustrates the effectiveness of the proposed method, and comparison and sensitivity analysis show the advantages of the proposed method.

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.

Multi-stage type-α constrained minimum-cost consensus for linguistic Z-number large-scale decision-making

As an extension of group decision-making in terms of scale and uncertainty, linguistic Z-number large-scale decision-making (LZ-LSDM) is emerging as a prominent research topic in the field of decision science. The unique structure of LZ-LSDM presents new challenges for both clustering analysis and consensus building. Minimum-cost consensus (MCC) based on the optimization principle is widely recognized as an effective tool for managing the consensus-reaching process. However, there is a scarcity of literature that addresses the study of MCC within the context of LZ-LSDM, as well as the application of MCC in the identification and treatment of non-cooperative behaviors. To this end, this study proposes a punishment strategy-driven multi-stage type-α constrained MCC model for LZ-LSDM problems. First, a similarity constraint-based clustering method with linguistic Z-numbers is proposed. Given the clustering results, a type-α constrained MCC (α-CMCC) model with personalized feedback constraints is designed to provide a personalized solution for visualizing opinion adjustment and preventing over-adjustment. Based on the optimal solution obtained by α-CMCC, the identification rule for non-cooperative behaviors is proposed. We conclude three punishment strategies—namely, pure, mixed, and cross—to address non-cooperative behaviors by arranging and combining commonly used punishment approaches. Finally, we illustrate the feasibility and validity of the model through a case study designed to facilitate consensus among an online patient community on knowledge-based recommendations. An exhaustive comparative analysis reveals the advantages and features of the proposed consensus model.

A Minimum Cost Consensus Model With Linguistic Information in an Asymmetric Costs Context to Prevent Manipulative Behavior for Emergency Decision Making

A Minimum Cost Consensus Model With Linguistic Information in an Asymmetric Costs Context to Prevent Manipulative Behavior for Emergency Decision Making

Optimal resources allocation to support the consensus reaching in group decision making

In group decision making (GDM), the minimum cost consensus model (MCCM) to assist a group to reach a consensus with the minimum cost has gained widespread attention. However, determining the unit costs for adjusting decision makers’ opinions in the MCCM is a challenging problem that limits its practical applications. Meanwhile, the MCCM is not modeled as a resources allocation problem in an explicit manner, and the opinions in the MCCM do not represent utilities/satisfactions, leading to the unclear implications of opinions’ adjustments. To overcome these limitations of the MCCM, this paper proposes the optimal resources allocation consensus model (ORACM) to assist the moderator to allocate resources without determining unit costs to support consensus reaching, through the introduction of the resources allocation problem and utility functions in its modeling. Furthermore, we present a theoretical analysis framework to reveal the properties of the ORACM and the connection between the ORACM and the MCCM, justifying the theoretical advantages of the ORACM. Moreover, the ORACM is applied to the transboundary river pollution control negotiations of Sichuan's Tuojiang River, and the effectiveness and feasibility of the ORACM are further validated with detailed simulation and comparison analyses.

A novel consensus model considering individual and social behaviors under the social trust network

In practical decision-making scenarios, the challenges lie in obtaining the collective opinion that the majority of decision makers are willing to accept, thereby arriving at the final decision result. Among them, both the inherent uncertainty and reliability embedded in the information may lead to a deviation from the fact in the final decision result. Moreover, individual and social behaviors have the potential to influence the acquisition of effective decision result. Based on this, this paper constructs a novel social network-based consensus model under discrete Z-number environment, taking into account the individual and social behaviors of experts. First, novel trust propagation and trust aggregation operators with discrete Z-numbers are developed, which aim to form a complete social trust network. Then, unit consensus cost function and compromise boundary function based on social trust network are given to objectively determine the unit adjustment costs and compromise boundaries of each decision maker. In addition, a minimum cost consensus model considering the coexistence and interaction between individual and social behaviors is explored. Last, the feasibility and superiority of the model are proved through a case of the agricultural supply chain. Through simulation and comparative analysis, the results show the effectiveness of novel trust propagation and aggregation operators. And the necessity of considering individual and social behaviors for consensus reaching process is presented.

A maximum satisfaction consensus-based large-scale group decision-making in social network considering limited compromise behavior

With the enrichment of social platforms, large-scale group decision-making (LSGDM) in social networks has gradually taken shape. In practice, experts may show limited compromise behavior during consensus reaching process (CRP), which may lead to bias or even failure in decision-making results. To tackle this issue, considering limited compromise behavior, this paper proposes a maximum satisfaction consensus (MSC) model, and focusing on LSGDM with fuzzy preference relation in social networks. Firstly, an expert weight determination algorithm integrating the interactive weights and individual weights is constructed. The interactive weights are determined by social influence strength, while the individual weights are measured by the compromise degree of limited compromise behavior and the consistency level of preferences. Subsequently, a grey clustering method is developed to classify experts into subgroups, considering both opinions similarity and limited compromise behavior similarity. In CRP, considering the limited compromise behavior, an MSC model under the limited budget determined by the minimum cost consensus (MCC) model is proposed. Based on MSC and MCC models, satisfaction-cost ratio is defined to measure the efficiency of CRP. Finally, a case study of selecting of shared bicycle operators and further discussion are conducted to verify the feasibility and superiority of the study.

Multi-dimensional multi-round minimum cost consensus models with iterative mechanisms involving reward and punishment measures

In order to address the issues of unfairness in consensus and subjectivity bias in data, while further expanding the traditional minimum cost consensus model (MCCM) in terms of opinion dimension and consensus round, we propose the multi-dimensional MCCM (MD-MCCM) and multi-round MCCM (MR-MCCM). Subsequently, we introduce the concepts and definitions pertaining to these two variants of consensus and formulate their respective consensus model frameworks. To benefit from the advantages of both, we integrate these two types of consensus models, thereby introducing the concept of multi-dimensional multi-round minimum cost consensus. To address the issues of unfairness and subjectivity in the consensus-reaching process, we propose two specific reward and punishment measures and devise the multi-dimensional multi-round consensus iterative mechanisms. These mechanisms facilitate an iterative update of decision-makers’ opinions, weights, and unit costs within the feedback process. Based on this foundation, we construct the multi-dimensional multi-round MCCM (MDMR-MCCM) involving Euclidean and Manhattan distance measures, and their corresponding algorithm and consensus reaching process are presented. Finally, a group decision problem concerning site selection validates the rationality and effectiveness of our models. Moreover, a comparative analysis of results obtained using different models is provided.

Robust two-stage minimum asymmetric cost consensus models under uncertainty circumstances

Group decision-making (GDM) problems in the real world are becoming more complex, and various uncertain factors exist. However, most scholars ignore the uncertainty in the GDM and the moderator cannot accurately predict the unit upward and downward adjustment costs of decision makers (DMs). To overcome these issues, this paper constructs the novel minimum cost consensus models with directional constraints (MCCM-DCs) based on robust optimization under uncertainty circumstances. Firstly, we construct two-stage asymmetric adjustment cost consensus models with better flexibility. The first stage focuses on establishing a consensus opinion, while the second stage entails deliberation on the adjustment deviations of the DMs. Further, considering the uncertainty of the unit adjustment cost, robust optimization is introduced to describe three different uncertainty scenarios in the second stage of the models. Then robust two-stage minimum asymmetric cost consensus models (TRMCCM-DCs) are proposed, which is closer to reality. Finally, the proposed models are applied to the case of water pollution control negotiations in the Taihu Basin in China, and further sensitivity analysis and comparison analysis are conducted to verify the validity of the models.

A Novel Robust Flexible Minimum Cost Consensus Model with Consensus Granule

A Novel Robust Flexible Minimum Cost Consensus Model with Consensus Granule

Robust minimum cost consensus models with uncertain asymmetric costs based on linear uncertain-constrained tolerance level

The ability of the minimum cost consensus model (MCCM) to promote consensus reaching in the domain of group decision-making (GDM) has been extensively studied. Recently, the MCCM has been enhanced by introducing the consensus principle and tolerance level to achieve a soft consensus. However, the potential impact of asymmetric and uncertain unit adjustment costs on the effectiveness of the consensus reaching process (CRP) has been overlooked. This paper aims to investigate the implications of uncertain asymmetric costs for achieving consensus with a certain level of tolerance, where new robust MCCMs with uncertain asymmetric costs are constructed under four uncertainty sets for the unit adjustment costs. Considering the linear uncertain-constrained tolerance level and consensus level, we incorporate the insight of an expert with a cost-free threshold into models. Additionally, through a pollutant emission application, the proposed robust MCCMs are able to effectively handle uncertainties arising from costs and improve the quality of the CRP compared to the traditional models. Finally, we conduct simulation experiments and sensitivity analysis to illustrate the effectiveness of the proposed models on achieving a consensus by identifying appropriate parameters.

A large-scale group decision-making method based on improved affinity propagation algorithm and adjustable minimum-cost consensus model in social networks

The rapid development of information technology has made social network large-scale group decision-making (SN-LSGDM) a focus of the field of decision science. Clustering and consensus-reaching process (CRP) are widely used methods in SN-LSGDM. In this paper, we propose an improved affinity propagation (AP) clustering algorithm that fully consider the trust and similarity attributes to obtain clustering results that are more in line with the expert preferences. Furthermore, we propose an adjustable minimum-cost consensus (MCC) model that considers trust-polymerization degree, which takes into account variations in expert weights and cluster diversity. And the cuckoo search (CS) algorithm is utilized to solve the model. Finally, the applicability and advantages of the proposed methods are demonstrated through a case and comparative analysis.

Multi-round minimum cost consensus model with objectivity-fairness driven feedback mechanism

In traditional group decision-making (GDM) and consensus reaching process (CRP), it may raise the issue of fairness for the moderator to subjectively assign each decision-maker’s (DM’s) weight and unit cost, and it is sometimes difficult to reach consensus with only one round of the CRP. In this paper, the impact of the aforementioned situations on the consensus is first analyzed, and then two specific improvement methods are accordingly provided. Based on which, the definitions of DM’s closeness centrality, affiliated subgroup as well as individual consensus level are given, and some incentives and penalties regarding DM’s weight and unit cost are used during the CRP, so as to improve the applicability and operability of the minimum cost consensus (MCC) in practical GDM problems while ensuring the fairness among DMs and the objectivity of data. Moreover, the single-round MCC is extended into the multi-round MCC by virtue of designing iterative methods on DM’s opinion, weight and unit cost, building the multi-round minimum cost consensus model (MRMCCM) with objectivity-fairness driven feedback mechanism, and presenting a detailed procedure alongside its algorithm of the multi-round CRP. Finally, a comprehensive evaluation case of financial product under the multi-round consensus validates the effectiveness and practicality of the new proposal, while its comparative analysis with other consensus models shows that the MRMCCM and the CRP with feedback mechanism help motivate DMs to reach higher-quality consensus at lower cost.

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.

Social network-driven bi-level minimum cost consensus model for large-scale group decision-making: A perspective of structural holes

Social network-driven bi-level minimum cost consensus model for large-scale group decision-making: A perspective of structural holes

Large-scale group decision consensus under social network: A chance-constrained robust optimization-based minimum cost consensus model

Large-scale group decision consensus under social network: A chance-constrained robust optimization-based minimum cost consensus model

Minimum Cost Consensus With Altruism Utility Constraints in Social Network Group Decision Making

In group decision making (GDM), considering the individuals’ satisfaction (i.e., utilities) about the consensus result is important. However, this issue is ignored by the extant minimum cost consensus models (MCCMs). Altruism describes a way of behaving that the individuals unselfishly concern for the utilities of others. Inspired by this, in this article we discuss the minimum cost consensus problem in social network GDM (SNGDM), where the utility constraints based on altruism are first incorporated. In SNGDM, altruism is reflected as the individuals will take both their personal utility and the utilities of others who connected with them into account to form their total utility. Based on this, we first define the individuals’ altruistic utility functions in the consensus process of SNGDM, and we propose several interesting properties of the proposed utility function. Afterward, we present a novel MCCM in SNGDM with opinion dynamics and altruistic utility (MCCM-OD-AU). Notably, in the proposed model, the deviation of opinion adjustment in the consensus process is measured as a psychological distance perceived by the individuals. Furthermore, some simulation studies and comparative analysis are conducted to investigate the effects of the altruistic behavior and the psychological distance of opinion adjustment on the consensus reaching results. Finally, two numerical studies, including an illustrative example and an application in energy-saving target formulation with real-world social network data, are provided to justify the performance of our proposal.

Blockchain-Enabled Trust Building for Managing Consensus in Linguistic Opinion Dynamics

To manage consensus in opinion dynamics models (ODMs), removing bias from agents' interactions and considering their willingness are critical. It can be accomplished by providing a secure mechanism that does not disclose agents' identities and opinions in their interactions, eliminating the impact of opinion similarity on trust building. To build trust and consensus opinion, we propose a linguistic ODM based on Blockchain technology. This model allows agents' opinions to be expressed using Z-numbers, as opposed to regular ODMs with numerical opinions. Agents are encouraged to modify their initial opinions in response to a minimum cost consensus model. Willingness of agents to accept or refuse the suggested modifications is realized through a Blockchain regime to avoid bias. The regime, however, must be supported by a trust-building mechanism to persuade agents to alter their opinions. To this end, we propose a Blockchain-enabled trust-building mechanism to improve agents' trust and guide them towards a consensus opinion. Following a sensitivity analysis of the underlying assumptions in the developed model, the proposed ODM is tested for its efficiency and validity.