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

Jiří Močkoř and David Hýnar
Additional contact information
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

Mathematics, 2021, vol. 9, issue 4, 1-26

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.

Keywords: hesitant fuzzy sets; intuitionistic fuzzy sets; fuzzy soft sets; monads in categories; monadic relations; Kleisli category (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/4/447/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/4/447/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:4:p:447-:d:504304

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().