Intuitionistic Fuzzy Rough Sets And Intuitionistic Fuzzy Topology Spaces

In this paper, we mainly study the relationship between intuitionistic fuzzy rough approximation spaces and intuitionistic fuzzy topological spaces. First, we investigate the mathematical structure of the set of all (inner, outer) definable sets in intuitionistic fuzzy approximation space. Then we study the intuitionistic fuzzy topology generated by a special intuitionistic fuzzy approximation space and the intuitionistic fuzzy approximation space generated by an intuitionistic fuzzy topology satisfying TC axiom. And then we discuss the relationship between intuitionistic fuzzy topologies generated by special intuitionistic fuzzy approximation spaces and intuitionistic fuzzy approximation spaces generated by intuitionistic fuzzy topologies satisfying TC axiom. Finally, we show the one to one correspondence between the set of all reflexive and transitive intuitionistic fuzzy relations which satisfy Tits (defined by Equ. (3)) holding TC axiom and the set of all intuitionistic fuzzy topologies satisfying TC axiom on the same universe of discourse.