Topological structures of rough sets over fuzzy lattices

A topological space can be described by using the closure operator. It is well known that there exists a close relationship between the closure operator and the upper approximation operator, that is, the upper approximation operators of rough set of the reflexive and transitive binary relation satisfy the Kuratowski closure axioms and vice versa. In this paper, we discuss generalizations of rough set approximation operators in fuzzy lattices, and show that there exists a similar relation between the closure operator and the upper approximation operator in fuzzy lattices.