Refined Pythagorean Fuzzy Sets: Properties, Set-Theoretic Operations and Axiomatic Results

Authors

  • Muhammad Saeed Department of Mathematics, University of Management and Technology, Pakistan https://orcid.org/0000-0002-7284-6908
  • Muhammad Rayees Ahmad Department of Mathematics, University of Management and Technology, Pakistan
  • Atiqe Ur Rahman Department of Mathematics, University of Management and Technology, Pakistan https://orcid.org/0000-0001-6320-9221

DOI:

https://doi.org/10.47852/bonviewJCCE2023512225

Keywords:

fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set

Abstract

Refined Pythagorean fuzzy set is the generalization of fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, refined fuzzy set, and refined intuitionistic fuzzy set as it not only bears the characteristics of these models but also addresses their limitations for real-life scenarios with sub-grades corresponding to membership and non-memberships grades. In order to equip the existing literature with conceptual framework of refined Pythagorean fuzzy sets, essential properties, set-theoretic operations, and axiomatic results are characterized with the help of numerical examples.

 

Received: 22 December 2021 | Revised: 22 January 2022 | Accepted: 25 January 2022

 

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.

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Published

2022-01-25

How to Cite

Saeed, M., Ahmad, M. R., & Rahman, A. U. (2022). Refined Pythagorean Fuzzy Sets: Properties, Set-Theoretic Operations and Axiomatic Results. Journal of Computational and Cognitive Engineering, 2(1), 10–16. https://doi.org/10.47852/bonviewJCCE2023512225

Issue

Vol. 2 No. 1 (2023)

Section

Research Articles

License

Copyright (c) 2022 Authors

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This work is licensed under a Creative Commons Attribution 4.0 International License.