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A unified ranking method of intuitionistic fuzzy numbers and Pythagorean fuzzy numbers based on geometric area characterization

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Abstract

The main purpose of this paper is to unify intuitionistic fuzzy numbers (IFNs) into Pythagorean fuzzy numbers (PFNs) environment through the coordinate mapping, and establish a novel unified ranking method for some defects of sorting standards of the current popular IFNs and PFNs. The new score function or accuracy function cannot only overcome the defects of the existing methods, but also realize the overall ranking of PFNs by calculating the geometric area. In this paper, the internal relationship between Pythagorean fuzzy set (PFS) and PFN was first explained based on algebraic and geometric methods, and some defects in the current ranking criteria of IFNs and PFNs were pointed out through counterexamples. IFNs and PFNs were mapped to the point coordinates in the unit circle of the first quadrant by coordinate transformation. Second, under the Pythagorean fuzzy number environment, the new score function and accuracy function were proposed by calculating area of geometric region and geometric analysis, their rationality are proved by strict mathematical theory, and a new ranking criterion for PFNs is given. Finally, as an application example, some PFNs are randomly selected in the Pythagorean fuzzy environment, the superiority of the proposed method is illustrated by comparing with other three different ranking methods. The result shows that the proposed method not only overcomes the contradiction between the independent ranking of traditional IFNs and PFNs, but also the ranking results are more in line with the reality.

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Authors and Affiliations

  1. 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

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  1. Yanhong Li
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  2. Gang Sun
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Correspondence to Gang Sun.

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Communicated by Susana Montes.

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

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Li, Y., Sun, G. A unified ranking method of intuitionistic fuzzy numbers and Pythagorean fuzzy numbers based on geometric area characterization. Comp. Appl. Math. 42, 16 (2023). https://doi.org/10.1007/s40314-022-02153-1

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