Continuous Fuzzy Relations in Fuzzy Topological Spaces

The notion of a continuous MV-valued fuzzy relation in Chang topological fuzzy space is defined, and the category \(\textbf{Top}\) of these spaces with continuous fuzzy relations as morphisms is presented. Equivalent conditions are presented for the fuzzy relation between two fuzzy topological structures to be continuous. Two special subcategories of \(\textbf{Top}\) are introduced, based on the category of fuzzy approximation spaces and the category of fuzzy partitions, both with fuzzy relations as morphisms.