On topological structure of T-fuzzy rough sets

This paper is to solve the problem under which assumptions a given pair of T-fuzzy rough approximation operators can induce a fuzzy topological space. It is proved that the set of all T-lower fuzzy rough approximation sets based on a fuzzy approximation space forms a fuzzy topology if and only if the fuzzy relation in the fuzzy approximation space is reflexive and T-transitive; and conversely, for a fuzzy topological space with some basic requirements, there exists a fuzzy reflexive and T-transitive approximation space such that the set of all T-lower fuzzy rough approximation sets in the approximation space is exactly the given fuzzy topology.