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

Mathematics

Jiří Močkoř¹  David Hýnar² 

[1] Institute for Research and Application of Fuzzy Modeling, University of Ostrava, 30.dubna 22, 702 00 Ostrava, Czech Republic;Varroc Lighting Systems, 74242 Šenov u Nového Jičína, Czech Republic;

关键词: hesitant fuzzy sets;    intuitionistic fuzzy sets;    fuzzy soft sets;    monads in categories;    monadic relations;    Kleisli category;   

DOI  :  10.3390/math9040447

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown