Groupoids in Categories of Fuzzy Topological Spaces with Continuous Fuzzy Relations

The notion of a continuous MV-valued fuzzy relation in Chang topological fuzzy spaces is defined, and the category \(\textbf{Top}\) of these spaces with continuous fuzzy relations as morphisms is presented. Two special subcategories of \(\textbf{Top}\) are presented, using the category of approximation spaces and the category of fuzzy partitions, both with fuzzy relations as morphisms. The concept of a fuzzy groupoid is defined for objects of these categories using the notion of fuzzy products in these subcategories.