Fuzzy type relations and transformation operators defined by monads

Abstract

Using the theory of monads in categories and the theory of monadic relations, the concept of general transformation operator defined by a monadic relation is introduced. It is proven that a number of standard relations used in categories of fuzzy structures are monadic relations for monads defined in these categories. It is also proven that a number of standardly used transformation operators in fuzzy sets, fuzzy rough sets, or fuzzy soft sets are in the form of general operators defined by monadic relations.