Pythagorean Fuzzy Entropy and Its Application in Multiple-Criteria Decision-Making


In this paper, a Pythagorean fuzzy decision-making method based on overall entropy is presented. First, a new definition is proposed for fuzzy entropy for any given Pythagorean fuzzy set (PFS). The proposed definition is based on the relationship between the fuzziness contained in the given PFS and the distance from a point to a line on a projection plane. Some related properties are introduced. Second, the overall entropy of the PFS is determined based on fuzzy entropy and the degree of hesitancy; proofs are presented to formalize some related properties. Third, an entropy weight formula is provided that is based on overall entropy, and a Pythagorean fuzzy decision-making method is developed on this basis. Finally, the effectiveness and practicability of the proposed methods are illustrated by an example and three comparative analyses.

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Data Availability Statement

All data are included in the manuscript.


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The authors are very grateful to the editor in chief and anonymous referees for their insightful and constructive comments and suggestions, which have been helpful in improving the paper. This research is supported by the Natural Science Foundation of Anhui Province of China (No.1908085MA07).

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Correspondence to Hui Zhang.

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Xu, T., Zhang, H. & Li, B. Pythagorean Fuzzy Entropy and Its Application in Multiple-Criteria Decision-Making. Int. J. Fuzzy Syst. 22, 1552–1564 (2020).

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  • Pythagorean fuzzy set
  • Fuzzy entropy
  • Overall entropy