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

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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.

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Acknowledgments

This work was supported by the grant (No. 71871149) from NSF of China, the supported by Guangdong Pearl River Scholars Chair Professor Plan, and the grant (No. 2020YJ0043) from Science and technology project of Sichuan Province.

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Authors and Affiliations

  1. School of Data Science and Artificial Intelligence, Dongbei University of Finance and Economics, Dalian, 116025, China

    Wenqi Liu

  2. Business School, Hohai University, Nanjing, 211100, China

    Hengjie Zhang

  3. Business School, Sichuan University, Chengdu, 610065, China

    Haiming Liang & Yucheng Dong

  4. School of Economics and Management, Southwest Jiaotong University, Chengdu, 610031, China

    Cong-cong Li

  5. School of Management, Shenzhen Institute of Information Technology, Shenzhen, 518172, China

    Yucheng Dong

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  1. Wenqi Liu
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  2. Hengjie Zhang
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  3. Haiming Liang
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  4. Cong-cong Li
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  5. Yucheng Dong
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Correspondence to Yucheng Dong.

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Liu, W., Zhang, H., Liang, H. et al. Managing Consistency and Consensus Issues in Group Decision-Making with Self-Confident Additive Preference Relations and Without Feedback: A Nonlinear Optimization Method. Group Decis Negot 31, 213–240 (2022). https://doi.org/10.1007/s10726-021-09766-7

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