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Geometric Ranking of Pythagorean Fuzzy Numbers Based on Upper Curved Trapezoidal Area Characterization Score Function

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Abstract

Pythagorean fuzzy number (PFN) is not only an extension of traditional intuitionistic fuzzy number (IFN), but also can deal with the decision-making problem of multi-attribute information in a wider range. In recent years, it has been rapidly developed and popularized in the field of decision science. Firstly, it is pointed out that there are some defects in the existing score function and ranking criteria of PFNs through counter examples, and the main causes of these defects are analyzed according to the geometric method. Secondly, IFNs are unified into the Pythagorean fuzzy environment, the new unified score function and geometric ranking criterion of IFNs and PFNs are proposed by the corresponding upper curved trapezoidal area and hesitation factor, and then the rationality of geometric ranking method and some basic properties of the score function are studied. Finally, the comparison of other ranking methods shows that the proposed method only needs a score function and its own hesitation to rank all PFNs uniformly, especially the accurate comparisons among equivalent PFNs are realized. This not only overcomes the contradiction and confusion caused by the respective ranking of traditional IFNs and PFNs, but also provides a theoretical basis for further expanding the fuzzy decision-making method of Pythagorean fuzzy sets.

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Funding

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

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Authors and Affiliations

  1. Department of Mathematics, Teacher’s College, Liaodong University, Dandong, 118003, Liaoning, China

    Yanhong Li

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

    Gang Sun

  3. School of Management, Tianjin Normal University, Tianjin, 300387, China

    Xiaoping Li

Authors
  1. Yanhong Li
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  2. Gang Sun
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  3. Xiaoping Li
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Correspondence to Gang Sun or Xiaoping Li.

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Li, Y., Sun, G. & Li, X. Geometric Ranking of Pythagorean Fuzzy Numbers Based on Upper Curved Trapezoidal Area Characterization Score Function. Int. J. Fuzzy Syst. 24, 3564–3583 (2022). https://doi.org/10.1007/s40815-022-01359-z

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  • DOI: https://doi.org/10.1007/s40815-022-01359-z

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