Managing Consistency and Consensus Issues in Group Decision-Making with Self-Confident Additive Preference Relations and Without Feedback: A Nonlinear Optimization Method

Wenqi Liu (), Hengjie Zhang (), Haiming Liang (), Cong-cong Li () and Yucheng Dong ()
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Wenqi Liu: Dongbei University of Finance and Economics
Hengjie Zhang: Hohai University
Haiming Liang: Sichuan University
Cong-cong Li: Southwest Jiaotong University
Yucheng Dong: Sichuan University

Group Decision and Negotiation, 2022, vol. 31, issue 1, No 10, 213-240

Abstract: Abstract Preference relations are one of the most common tools used to represent decision makers’ preferences. Self-confident preference relations, whose preference elements include self-confidence levels and preference values, is a new and effective tool that can be used to express decision makers’ self-confidence levels in the preference relation. When using self-confident preference relations in group decision-making problems, the individual consistency and group consensus are two fundamental issues. To deal with these issues, a consistency index is proposed to measure the consistency level of a self-confident additive preference relation. Meanwhile, a consensus index is presented to measure the group consensus level of self-confident additive preference relations. Subsequently, two nonlinear optimization methods are developed to manage consistency and consensus issues for group decision-making within the context of consensus reaching without feedback. The first model is used to derive self-confident additive preference relations with acceptable consistency, and the second optimization model is employed to promote consensus reaching that simultaneously manage individual consistency. A hypothetical application with comparative analysis is conducted to show the usability and validity of the proposed methods.

Keywords: Group decision making; Consensus; Consistency; Self-confidence; Additive preference relations; Optimization (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10726-021-09766-7

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