Novel distance measures for Pythagorean fuzzy sets with applications to pattern recognition problems

Abstract

Pythagorean fuzzy set (PFS) is a concept that generalizes intuitionistic fuzzy sets. The notion of PFSs is very much applicable in decision science because of its unique nature of indeterminacy. The main feature of PFSs is that it is characterized by membership degree, non-membership degree, and indeterminate degree in such a way that the sum of the square of each of the parameters is one. In this paper, we propose some novel distance measures for PFSs by incorporating the conventional parameters that describe PFSs. We provide a numerical example to illustrate the validity and applicability of the distance measures for PFSs. While analyzing the reliability of the proposed distance measures in comparison with similar distance measures for PFSs in the literature, we discover that the proposed distance measures, especially, \(d_5\) yields the most reasonable measure. Finally, some applications of \(d_5\) to pattern recognition problems are explicated. These novel distance measures for Pythagorean fuzzy sets could be applied in decision making of real-life problems embedded with uncertainty.

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Acknowledgements

The authors are thankful to the Editors-in-chief, Professors Withold Pedrycz and Shyi-Ming Chen for their technical comments, and to the anonymous reviewers for their suggestions, which have improved the quality of the paper.

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Ejegwa, P.A., Awolola, J.A. Novel distance measures for Pythagorean fuzzy sets with applications to pattern recognition problems. Granul. Comput. 6, 181–189 (2021). https://doi.org/10.1007/s41066-019-00176-4

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Keywords

  • Distance measure
  • Fuzzy set
  • Intuitionistic fuzzy set
  • Pattern recognition
  • Pythagorean fuzzy set