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

Autor: Mei-Yu Qiu, Cai-Xia Huang, Fang Liu
Rok vydání: 2021
Předmět:
Zdroj: International Journal of Fuzzy Systems. 24:355-370
ISSN: 2199-3211
1562-2479
DOI: 10.1007/s40815-021-01140-8
Popis: 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.
Databáze: OpenAIRE
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