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Extended Fuzzy Sets and Their Applications

Author

Listed:
  • Bahram Farhadinia

    (Department of Mathematics, Quchan University of Technology, Razavi Khorasan Province, Quchan 9477177870, Iran)

  • Francisco Chiclana

    (Institute of Artificial Intelligence, De Montfort University, Leicester LE1 9BH, UK
    Andalusian Research Institute on Data Science and Computational Intelligence (DaSCI), University of Granada, 18071 Granada, Spain)

Abstract

This contribution deals with introducing the innovative concept of extended fuzzy set (E-FS), in which the S-norm function of membership and non-membership grades is less than or equal to one. The proposed concept not only encompasses the concept of the fuzzy set (FS), but it also includes the concepts of the intuitionistic fuzzy set (IFS), the Pythagorean fuzzy set (PFS) and the p-rung orthopair fuzzy set (p-ROFS). In order to explore the features of the E-FS concept, set and algebraic operations on E-FSs, average and geometric operations of E-FSs are studied and an E-FS score function is defined. The superiority of the E-FS concept is further confirmed with a score-based decision making technique in which the concepts of FS, IFS, PFS and p-ROFS do not make sense.

Suggested Citation

  • Bahram Farhadinia & Francisco Chiclana, 2021. "Extended Fuzzy Sets and Their Applications," Mathematics, MDPI, vol. 9(7), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:770-:d:529085
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