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A Quantification Approach to Flexibility Degrees of Fuzzy Numbers and Its Application to Group Decision Making

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Abstract

A certain flexibility of decision makers (DMs) is usually requisite for reaching the consensus in group decision making (GDM). When the judgments of DMs are expressed as fuzzy-valued quantities, the required flexibility has been shown. In this paper, we report a quantification approach to flexibility degrees (FDs) of fuzzy numbers and a consensus model in GDM with fuzzy-valued judgments. First, an axiomatic definition of FDs is proposed for fuzzy numbers. Based on a bounded positive scale, the novel formulae are constructed for quantifying the FDs of interval numbers, triangular fuzzy numbers (TFNs), and trapezoidal fuzzy numbers (TPFNs), respectively. The effects of the prototypical values of TFNs and TPFNs on the FDs are addressed. Second, by considering confidence levels and multiplicative reciprocity, the FD of triangular fuzzy multiplicative reciprocal preference relations (TFMRPRs) is calculated. A flexibility-degree-driven operator is provided to aggregate individual TFMRPRs. Third, the consensus degree of DMs is defined and a nonlinear optimization model is constructed to achieve the largest consensus degree. A new algorithm for the consensus model in GDM is elaborated on and the case study is made to illustrate the proposed method. Finally, the sensitivity of the centroid of TFNs on the final solution of a GDM problem is analyzed by numerical examples. The observations reveal that the position of the centroid plays a great role on the FD of TFNs.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China (Nos. 71871072, 71571054), 2017 Guangxi high school innovation team and outstanding scholars plan, the Guangxi Natural Science Foundation for Distinguished Young Scholars (No. 2016GXNSFFA380004), and the Innovation Project of Guangxi Graduate Education (No. YCSW2021044).

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  1. School of Mathematics and Information Science, Guangxi University, Nanning, 530004, Guangxi, China

    Fang Liu, Cai-Xia Huang & Mei-Yu Qiu

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  1. Fang Liu
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Correspondence to Fang Liu.

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Liu, F., Huang, CX. & Qiu, MY. A Quantification Approach to Flexibility Degrees of Fuzzy Numbers and Its Application to Group Decision Making. Int. J. Fuzzy Syst. 24, 355–370 (2022). https://doi.org/10.1007/s40815-021-01140-8

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  • DOI: https://doi.org/10.1007/s40815-021-01140-8

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