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Isomorphic Operators and Ranking Methods for Pythagorean and Intuitionistic Fuzzy Sets

In: Pythagorean Fuzzy Sets

Author

Listed:
  • Yi Yang

    (Institute of Big Data and Internet Innovation, Hunan University of Technology and Business, Key Laboratory of Hunan Province for New Retail Virtual Reality Technology)

  • Zhen-Song Chen

    (Wuhan University, School of Civil Engineering)

Abstract

With three pairs of fuzzy sets, intuitionistic fuzzy sets and Pythagorean fuzzy sets, interval-valued intuitionistic fuzzy sets and interval-valued Pythagorean fuzzy sets, dual hesitation fuzzy sets, and dual hesitation Pythagorean fuzzy sets as the research objects, the isomorphic relation between each pair of fuzzy sets is studied from three aspects, such as operational laws, aggregation operators, and ranking methods. Firstly, based on an automorphism on the unit interval, the transformation relationship between intuitionistic fuzzy dual triple (TI, SI, NI) and Pythagorean fuzzy dual triple (TP, SP, NP) is investigated, and the mathematical isomorphism for each pair of fuzzy sets is developed. Subsequently, the isomorphic operations for these three pairs of fuzzy sets are provided, which lays the foundation for the operators’ isomorphism. Secondly, the isomorphic Archimedean aggregation operators of each pairs of fuzzy sets are constructed based on the isomorphic operational laws. Finally, the isomorphism ranking methods are developed by exploring the conversion relationship between the score function and the accuracy function of each pair of fuzzy sets.

Suggested Citation

  • Yi Yang & Zhen-Song Chen, 2021. "Isomorphic Operators and Ranking Methods for Pythagorean and Intuitionistic Fuzzy Sets," Springer Books, in: Harish Garg (ed.), Pythagorean Fuzzy Sets, pages 107-144, Springer.
    • Handle: RePEc:spr:sprchp:978-981-16-1989-2_5
    DOI: 10.1007/978-981-16-1989-2_5
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