Consensus Reaching Research Articles

A Consensus Reaching Process for Product Design Decision-Making by Integrating Intuitionistic Fuzzy Sets and Trust Network

A Consensus Reaching Process for Product Design Decision-Making by Integrating Intuitionistic Fuzzy Sets and Trust Network

Consensus Reaching with Dynamic Trust Relationships and Cost-Learning in Group Decision Making

Consensus Reaching with Dynamic Trust Relationships and Cost-Learning in Group Decision Making

Graph Model for Conflict Resolution With Internal Consensus Reaching and External Game

Graph Model for Conflict Resolution With Internal Consensus Reaching and External Game

An Integrated CREAM for Human Reliability Analysis Based on Consensus Reaching Process under Probabilistic Linguistic Environment

Human reliability analysis (HRA) is widely used to evaluate the impact of human errors on various complex human–machine systems for enhancing their safety and reliability. Nevertheless, it is hard to estimate the human error probability (HEP) in reality due to the uncertainty of state assessment information and the complex relations among common performance conditions (CPCs). In this paper, we aim to present a new integrated cognitive reliability and error analysis method (CREAM) to solve the HRA problems under probabilistic linguistic environment. First, the probabilistic linguistic term sets (PLTSs) are utilized to handle the uncertain task state assessments provided by experts. Second, the minimum conflict consensus model (MCCM) is employed to deal with conflict task state assessment information to assist experts reach consensus. Third, the entropy weighting method is used to determine the relative objective weights of CPCs. Additionally, the CPC effect indexes are introduced to assess the overall effect of CPCs on performance reliability and obtain the HEP estimation. Finally, the reliability of the proposed CREAM is demonstrated via a healthcare practical case. The result shows that the new integrated CREAM can not only effectively represent experts’ uncertain task state assessments but also determine more reliable HEP estimation in HRA.

A Feedback Mechanism With Unknown Bounded Confidence-Based Optimization Model for Consensus Reaching in Social Network Group Decision Making

A Feedback Mechanism With Unknown Bounded Confidence-Based Optimization Model for Consensus Reaching in Social Network Group Decision Making

Supporting Consensus Reaching on Prioritizing Failure Modes in Reliability Management: The Role of Social-Trust-Driven Rating Modifications Willingness

Supporting Consensus Reaching on Prioritizing Failure Modes in Reliability Management: The Role of Social-Trust-Driven Rating Modifications Willingness

Threshold-Based Value-Driven Method to Support Consensus Reaching in Multicriteria Group Sorting Problems: A Minimum Adjustment Perspective

In multicriteria group decision-making (MCGDM) problems, there exist the situations that alternatives need to be assigned to several predefined ordered categories rather than be ranked from the most preferred to the least preferred, which is called multicriteria group sorting problems. To address multicriteria group sorting problems, it is necessary to implement a consensus reaching process to fully consider the opinion of each decision maker and reduce the conflict among them. To do so, this article proposes a consensus reaching model for multicriteria group sorting problems based on the threshold-based value-driven sorting method from the perspective of minimum adjustment. Specifically, we first define the consensus measure to calculate the agreement degree among decision makers by considering the ordinal information and cardinal information at the same time. On this basis, we construct a minimum adjustment optimization model in terms of the threshold-based value-driven sorting method to assist decision makers in modifying their decision matrices and further promote consensus. Followed by this, an optimization model that aims to minimize the distance between all decision makers and the group with respect to alternatives’ comprehensive values and sorting results is developed to determine the group sorting result for alternatives. Moreover, a numerical application of urban park management, some sensitivity analysis, and simulation experiments are provided to justify the proposed method. Experimental results reveal that the proposed method is effective in promoting consensus.

Integrating incomplete preference estimation and consistency control in consensus reaching

In group decision making (GDM), there exists a situation in which experts may not able to provide comparative judgements regarding all pairs of alternatives, and therefore leading to the expression of incomplete preference. The existing frameworks to manage the GDM problem with incomplete preference relations have been investigated intensively and followed a common resolution scheme composed of three processes: estimation, consistency improvement, and consensus reaching. However, the consensus reaching process is applied after the estimation process and consistency improvement processes, leading to the destruction of the consistency of estimated preference relations, which will duplicate the process of improving consistency and consensus, resulting in significant adjustments of experts’ preferences. To avoid this issue, we first propose a joint framework to integrate the consensus reaching process with estimation and consistency improvement. This framework is designed based on a minimum adjustment optimization model with completeness, consistency, and consensus control. It can produce complete preference relations with acceptable consistency and consensus, and simultaneously guarantee the minimum adjustment of experts’ preferences. Finally, simulation and comparative analyses are used to justify the validity of the proposal.

Multisource Imprecise Information Calibration for Reliability Assessment of Multistate Systems: A Consensus Reaching Perspective

Multisource Imprecise Information Calibration for Reliability Assessment of Multistate Systems: A Consensus Reaching Perspective

Consensus Reaching Process for Traditional Group Decision Making in View of the Optimal Adjustment Mechanism.

Consensus reaching process (CRP) is a key topic in the area of group decision making (GDM). When the consensus level is not high enough, it becomes necessary to adjust the original opinions of decision makers (DMs). To offer the adjustment reference for DMs, we build the programming models to determine the minimum modification to be carried out from the individual and global perspectives. Meanwhile, all DMs are divided into two subgroups: DMs with acceptable and unacceptable consensus levels. If some DMs with unacceptable consensus level do not accept the relevant modifications, the Nash bargaining game-based programming model is built for the fairness and efficiency of modifications. When some DMs refuse to make any modifications or tend to modify the opinions in their way, with respect to different group consensus situations, we make the minimum hybrid penalty mechanism by the Nash bargaining game-based programming models. For each case, we determine the corresponding optimal modification mechanism in view of the fixed individual total modification and the maximum consensus level. Furthermore, we study the arrangements of weights of DMs according to their cardinal and ordinal consensus contributions. Based on these results, we present a new algorithm and illustrate its application by a numerical example. Moreover, we carry out the sensitivity and comparison analysis. We summarize the conclusions and future research directions in the end. The main originality of the new method includes: the fairness and efficiency of modifications, and the determination of the hybrid penalty mechanism.

Consensus Reaching in Group Decision Making With Linear Uncertain Preferences and Asymmetric Costs

Consensus reaching process (CRP), as an essential part of group decision making (GDM), can facilitate more effective consensus by taking human behaviors into account. Extending the established research on uncertain minimum cost consensus models (MCCMs), this article continues to adopt linear uncertainty distributions (LUDs) to represent decision-maker’s (DM’s) preference, but considers asymmetric costs into a new framework of CRP, where DM’s preference and weight are both adjusted according to democratic consensus. Moreover, in light of the uncertain distance measure, two novel optimization-based consensus models are built in this article: one is to obtain a minimum cost consensus by simultaneously considering asymmetric costs, aggregation function, and consensus measure; while the other provides a more flexible way to address GDM problems without presetting a specific consensus level (CL) threshold. Some 0–1 binary variables are further introduced to reduce the calculation complexity resulted from piecewise functions in the new multicoefficient goal programming models. Finally, an illustrative example and further discussion reveal the feasibility and superiority of our new method.

Reinforcement Learning-Based Feedback and Weight-Adjustment Mechanisms for Consensus Reaching in Group Decision Making

The number of discussion rounds and harmony degree of decision makers are two crucial efficiency measures to be considered in the design of the consensus-reaching process for the group decision-making problems. Adjusting the feedback parameter and importance weights of the decision makers in the recommendation mechanism has a great impact on these efficiency measures. This work aims to propose novel and efficient reinforcement learning-based adjustment mechanisms to address the tradeoff between the aforementioned measures. To employ these adjustment mechanisms, we propose to extract the dynamics of state transition from consensus models based on the distributed trust functions and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Z$ </tex-math></inline-formula> -Numbers in order to convert the decision environment into a Markov decision process. Two independent reinforcement learning agents are then trained via a deep deterministic policy gradient algorithm to adjust the feedback parameter and importance weights of decision makers. The first agent is trained toward reducing the number of discussion rounds while ensuring the highest possible level of harmony degree among the decision makers. The second agent merely speeds up the consensus reaching process by adjusting the importance weights of the decision makers. Various experiments are designed to verify the applicability and scalability of the proposed feedback and weight-adjustment mechanisms in different decision environments.

Consensus Reaching with Minimum Adjustment and Consistency Management in Group Decision Making with Intuitionistic Multiplicative Preference Relations

Consensus Reaching with Minimum Adjustment and Consistency Management in Group Decision Making with Intuitionistic Multiplicative Preference Relations

Consensus Reaching Process With Multiobjective Optimization for Large-Scale Group Decision Making With Cooperative Game

Large-scale group decision making (LSGDM) is a common decision-making activity in which experts elicit their preferences through preference relations with consistencies based on additive properties. LSGDM has become a popular topic in decision making because of its necessity and applicability in multiple fields. In LSGDM, the consensus reaching process (CRP) ensures that decision makers (DMs) agree on the final decision-making results. Therefore, it is significant to investigate the CRP to improve the LSGDM process. In this article, a new method for LSGDM that includes a clustering algorithm, a weight determination method, and a CRP is developed. First, based on the consensus and the consistency of the additive preference relation, the DMs are classified into different subgroups by using the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -means clustering algorithm. Then, because different subgroups have distinct decision-making interests, a weight determination method based on a cooperative game is proposed. Furthermore, to measure the consensus of each subgroup more comprehensively, the intra- and interconsensus levels are defined. These consensus levels are divided into four scenarios (acceptable–acceptable, acceptable–unacceptable, unacceptable–acceptable, and unacceptable–unacceptable) according to predetermined thresholds. Furthermore, different feedback mechanisms based on multiobjective optimization models corresponding to different CRP scenarios are presented. Finally, an illustrative example and comparative analyses are provided to verify the feasibility and validity of the proposed method.

Consensus Reaching With Minimum Cost of Informed Individuals and Time Constraints in Large-Scale Group Decision-Making

Consensus reaching process (CRP) is important and present in a wide range of application areas. In practical CRP, the managers (e.g., enterprise) often hire some informed individuals (e.g., persuaders) to promote the efficiency of consensus reaching. This article proposes a CRP with minimum cost of informed individuals and time constraint in large-scale group decision-making (LSGDM) with bounded confidence effects. The consensus model with bounded confidence effects (CBC model) is formulated. Then, desirable properties of the CBC model are discussed to facilitate its resolution. Next, an extended particle swarm optimization algorithm is designed to solve the CBC model. Finally, a numerical analysis, a comparison analysis, and a simulation analysis are provided to illustrate the feasibility and effectiveness of the proposed approach.

Personalized Individual Semantics-Based Consistency Control and Consensus Reaching in Linguistic Group Decision Making

Consistency and consensus are important issues for linguistic group decision making (GDM), which have been extensively studied by scholars. Nevertheless, most of previous consensus reaching models focus on adjusting decision makers’ preference relations and ignore the individual consistency, which results in that individual consistency may be destroyed by using these consensus reaching models. Moreover, it has been accepted that words mean different things for different people and thus, it is also necessary to model decision makers’ personalized individual semantics (PISs) in linguistic GDM. This work focuses on developing some PIS-based consistency control and consensus reaching models for linguistic GDM. First, we analyze the problems existing in previous PIS models and then develop a minimum adjustment-based optimization model to test and improve the individual consistency for a linguistic preference relation (LPR). Followed by this, a PIS-based individual consensus-level maximization model and a PIS-based minimum adjustment model are established for consensus reaching in linguistic GDM, in which individual consistency control is considered. Furthermore, an algorithm for consensus reaching is proposed based on these models. To justify the proposed models and algorithm, some numerical results and simulation analysis are provided eventually.

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.

Consensus Reaching Process for Group Decision Making with Distributed Preference Relations Under Fuzzy Uncertainty

Consensus Reaching Process for Group Decision Making with Distributed Preference Relations Under Fuzzy Uncertainty

A Personalized Feedback Mechanism Based on Bounded Confidence Learning to Support Consensus Reaching in Group Decision Making

Different feedback mechanisms have been reported in consensus reaching models to provide advices for preference adjustment to assist decision makers to improve their consensus levels. However, most feedback mechanisms do not consider the willingness of decision makers to accept these advices. In the opinion dynamics discipline, the bounded confidence model justifies well that in the process of interaction a decision maker only considers the preferences that do not exceed a certain confidence level compared to his own preference. Inspired by this idea, this article proposes a new consensus reaching model with personalized feedback mechanism to help decision makers with bounded confidences in achieving consensus. Specifically, the personalized feedback mechanism produces more acceptable advices in the two cases where bounded confidences are known or unknown, and the unknown ones are estimated by a learning algorithm. Finally, numerical example and simulation analysis are presented to explore the effectiveness of the proposed model in reaching consensus.

Balance Dynamic Clustering Analysis and Consensus Reaching Process With Consensus Evolution Networks in Large-Scale Group Decision Making

Large-scale group decision-making (LSGDM) solution is usually based on the clustering analysis process (CAP) and consensus reaching process (CRP). However, CAP and CRP can be contradictory since CAP is performed based on the differences between potentially small groups and CRP is conducted to improve the overall similarity of a large group. To balance CAP and CRP, a dynamic clustering analysis process (DCAP) based on consensus evolution networks is proposed. A clustering algorithm proposed based on community detection method can be used to handle the diverse network structures with dynamic consensus thresholds. The clustering validity based on the intracluster consensus levels in subgroups and the intercluster consensus level among subgroups is evaluated. Then, the DCAP after each feedback adjustment round in CRP is reanalyzed. In such a way, effective clustering can also be found after a satisfying consensus is reached. Finally, a case study shows the availability of this approach and comparative analyses are provided to highlight the advantages from both theoretical and numerical perspectives.