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Group decision-making with interval multiplicative preference relations

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Abstract

This paper discusses group decision-making (GDM) with interval multiplicative preference relations (IMPRs) based on the geometric consistency. We propose a logarithmically geometric compatibility degree between two IMPRs and then define a geometrically logarithmic consistency index of IMPRs. The new consistency index of IMPRs is invariant under permutation of alternatives and transpose of IMPRs. By the statistics theory, the thresholds of the geometrically logarithmic consistency index are provided. For an unacceptably consistent IMPR, an interactive iterative algorithm is designed to improve its consistency level. Using the relationship between an interval weight vector (IWV) and an IMPR, a fuzzy programming model is established to derive an IWV. This model is converted into a linear programming model for resolution. Subsequently, a new individual decision-making (IDM) method with an IMPR is put forward. By minimizing the logarithmically geometric compatibility degree between each individual IMPR and the collective one, a convex programming model is built to determine experts’ weights. Consequently, a novel GDM method with IMPRs is presented. Numerical examples and simulation experiments are conducted to reveal the superiority of the proposed IDM method and GDM method.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Nos. 62263012, 62141302 and 11861034), the Humanities Social Science Programming Project of Ministry of Education of China (No. 20YJA630059), The Natural Science Foundation of Jiangxi Province of China (No.20212BAB201011), The Science and Technology Research Project of Hubei Education Department (No. D20211303), the Philosophy and Social Science Project of Hubei Education Department (No. 20Y035).

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Authors and Affiliations

  1. School of Information Technology, Jiangxi University of Finance and Economics, Nanchang, 330013, China

    Shuping Wan

  2. School of Economics and Management, Yangtze University, Jingzhou, 434023, China

    Xianjuan Cheng

  3. School of Science, Shanghai Institute of Technology, Shanghai, 201418, China

    Jiuying Dong

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  1. Shuping Wan
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  2. Xianjuan Cheng
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  3. Jiuying Dong
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Contributions

Shuping Wan: Supervision, Writing- Reviewing and Editing Xianjuan Cheng: Conceptualization, Methodology, Writing- Original draft, Visualization Jiuying Dong: Software, Formal analysis.

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Correspondence to Xianjuan Cheng.

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Wan, S., Cheng, X. & Dong, J. Group decision-making with interval multiplicative preference relations. Knowl Inf Syst 65, 2305–2346 (2023). https://doi.org/10.1007/s10115-022-01816-z

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