Consistency and Consensus of Distributed Preference Relations Based on Stochastic Optimal Allocation in GDM Problems

IF 3.6 4区 管理学 Q2 MANAGEMENT
Xianchao Dai, Hao Li, Ligang Zhou
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Abstract

Consistency and consensus are two key challenges under uncertain circumstances in pairwise comparison-based group decision-making (GDM), especially in a distributed preference relation (DPR) environment. In this paper, a comprehensive framework designed to tackle GDM problems evaluated by DPR is developed. First, after discussing two types of inconsistency in a complete DPR matrix: uncertainty-caused inconsistency and preference-caused inconsistency, two targeted optimization models to generate a consistent certain DPR matrix are proposed based on the definitions of stochastic additive strong/weak consistency and the similarity measure between DPRs. These models can effectively derive a DPR matrix closest to the original certain judgment by stochastic optimal allocation of uncertainties. Second, a new group consensus degree is introduced to measure the consensus in the group. Then a consensus improving model is given to reach an acceptable consensus by adjusting the DPR matrix of the decision maker (DM) with the least consensus degree. Third, the DMs’ weights are determined based on the expected consistency of the original DPR matrix by stochastic simulation instead of subjective judgment, and then the aggregated DPR matrix is obtained to derive a final solution using the weighted averaging operator. Finally, an automobile selection example is given to verify the validity and rationality of the proposed models.

Abstract Image

基于 GDM 问题中随机最优分配的分布式偏好关系的一致性和共识性
在基于成对比较的群体决策(GDM)中,尤其是在分布式偏好关系(DPR)环境中,一致性和共识是不确定情况下的两大关键挑战。本文建立了一个综合框架,旨在解决由 DPR 评估的 GDM 问题。首先,在讨论了完整 DPR 矩阵中的两类不一致性:不确定性导致的不一致性和偏好导致的不一致性之后,根据随机相加强/弱一致性和 DPR 之间相似性度量的定义,提出了两个有针对性的优化模型来生成一致的特定 DPR 矩阵。这些模型可以通过随机优化分配不确定性,有效地得出最接近原始确定判断的 DPR 矩阵。其次,引入新的群体共识度来衡量群体中的共识。然后给出一个共识改进模型,通过调整共识度最小的决策者(DM)的 DPR 矩阵来达成可接受的共识。第三,通过随机模拟而非主观判断,根据原始 DPR 矩阵的预期一致性确定 DM 的权重,然后利用加权平均算子得到汇总的 DPR 矩阵,从而得出最终解决方案。最后,通过一个汽车选型实例来验证所提模型的有效性和合理性。
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来源期刊
CiteScore
5.70
自引率
6.70%
发文量
32
期刊介绍: The idea underlying the journal, Group Decision and Negotiation, emerges from evolving, unifying approaches to group decision and negotiation processes. These processes are complex and self-organizing involving multiplayer, multicriteria, ill-structured, evolving, dynamic problems. Approaches include (1) computer group decision and negotiation support systems (GDNSS), (2) artificial intelligence and management science, (3) applied game theory, experiment and social choice, and (4) cognitive/behavioral sciences in group decision and negotiation. A number of research studies combine two or more of these fields. The journal provides a publication vehicle for theoretical and empirical research, and real-world applications and case studies. In defining the domain of group decision and negotiation, the term `group'' is interpreted to comprise all multiplayer contexts. Thus, organizational decision support systems providing organization-wide support are included. Group decision and negotiation refers to the whole process or flow of activities relevant to group decision and negotiation, not only to the final choice itself, e.g. scanning, communication and information sharing, problem definition (representation) and evolution, alternative generation and social-emotional interaction. Descriptive, normative and design viewpoints are of interest. Thus, Group Decision and Negotiation deals broadly with relation and coordination in group processes. Areas of application include intraorganizational coordination (as in operations management and integrated design, production, finance, marketing and distribution, e.g. as in new products and global coordination), computer supported collaborative work, labor-management negotiations, interorganizational negotiations, (business, government and nonprofits -- e.g. joint ventures), international (intercultural) negotiations, environmental negotiations, etc. The journal also covers developments of software f or group decision and negotiation.
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