Chang fuzzy topological spaces; continuous fuzzy relation; approximation spaces; fuzzy partitions.

The notion of a continuous $MV$-valued fuzzy relation in Chang topological fuzzy space is defined, and the category $\bf Top$ 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 $\bf Top$ are introduced, based on the category of fuzzy approximation spaces and the category of fuzzy partitions, both with fuzzy relations as morphisms.