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TOPSIS Method Based on Hesitant Factor and Priority Weighted Operator in Pythagorean Fuzzy Environment

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Abstract

The main innovation of this paper is to transform Pythagorean fuzzy numbers (PFNs) into the analytic representation of centroid coordinates and hesitation factors through the transformation, and then the unified ranking method, distance measure and similarity with respect to PFNs are proposed using geometric method. These concepts can not only overcome some defects of existing methods, but also be applied to multi-attribute group decision-making problems. In this paper, the centroid coordinate representation of PFN is first introduced with regard to the hesitation region, when considering the degree of nonzero hesitation, the hesitation factor is proposed by comparing with the smallest element (0,1), and a new ranking method for PFNs is given by calculating the hesitation factor in the Pythagorean fuzzy number environment. Secondly, the distance measure and degree of similarity are put forward through the hesitation factor and centroid coordinates, and the Pythagorean fuzzy priority weighted average (PFPWA) operator is given by improving the priority weight parameter. Besides, the basic properties of PFPWA operator are discussed. Finally, the positive (negative) hesitation factor solutions, bidirectional projections and degrees of closeness for group comprehensive evaluation matrix are obtained, and a new TOPSIS method for dealing with multi-attribute decision-making problems is given under the Pythagorean fuzzy environment. The given example shows that the proposed method not only expands the scope of application and reduces the loss of some fuzzy information, but also eliminates the impact of abnormal data on the aggregation results by considering the priority of experts.

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Funding

This work has been supported by National Natural Science Foundation of China (Grant Nos. 61463019, 61374009) and Natural Science Foundation of Hunan Province (Grant No. 2019JJ40062).

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Authors and Affiliations

  1. School of Science, Hunan Institute of Technology, Hengyang, 421002, Hunan, China

    Gang Sun

  2. Junior High School of Zhumadian, Zhumadian, 463003, Henan, China

    Jing Luo

  3. School of Mathematical Science, Tianjin Normal University, Tianjin, 300387, China

    Guijun Wang

Authors
  1. Gang Sun
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  2. Jing Luo
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  3. Guijun Wang
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Correspondence to Guijun Wang.

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Sun, G., Luo, J. & Wang, G. TOPSIS Method Based on Hesitant Factor and Priority Weighted Operator in Pythagorean Fuzzy Environment. Int. J. Fuzzy Syst. 25, 831–850 (2023). https://doi.org/10.1007/s40815-022-01406-9

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  • DOI: https://doi.org/10.1007/s40815-022-01406-9

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