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On Unification of Methods in Theories of Fuzzy Sets, Hesitant Fuzzy Set, Fuzzy Soft Sets and Intuitionistic Fuzzy Sets

Author

Listed:
  • Jiří Močkoř

    (Institute for Research and Application of Fuzzy Modeling, University of Ostrava, 30.dubna 22, 70200 Ostrava, Czech Republic)

  • David Hýnar

    (Varroc Lighting Systems, 74242 Šenov u Nového Jičína, Czech Republic)

Abstract

The main goal of this publication is to show that the basic constructions in the theories of fuzzy sets, fuzzy soft sets, fuzzy hesitant sets or intuitionistic fuzzy sets have a common background, based on the theory of monads in categories. It is proven that ad hoc defined basic concepts in individual theories, such as concepts of power set structures in these theories, relations or approximation operators defined by these relations are only special examples of applications of the monad theory in categories. This makes it possible, on the one hand, to unify basic constructions in all these theories and, on the other hand, to verify the legitimacy of ad hoc definitions of these constructions in individual theories. This common background also makes it possible to transform these basic concepts from one theory to another.

Suggested Citation

  • Jiří Močkoř & David Hýnar, 2021. "On Unification of Methods in Theories of Fuzzy Sets, Hesitant Fuzzy Set, Fuzzy Soft Sets and Intuitionistic Fuzzy Sets," Mathematics, MDPI, vol. 9(4), pages 1-26, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:447-:d:504304
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    References listed on IDEAS

    as
    1. Huimin Zhang, 2014. "Linguistic Intuitionistic Fuzzy Sets and Application in MAGDM," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-11, April.
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