On topological properties of generalized rough sets

摘要

In this note we consider topological properties of generalized rough sets. In any approximation space (X, R) of a generalized rough set we show that 1. If R is reflexive, then the set O_R = {A is contained in X|R_-(A) = A} defined by R_- is a topology on X; 2. If R is reflexive and symmetric, then the topology O_R has the following property (Clop) A : open <=> A : closed 3. Conversely, for any topology O with (Clop), there is a reflexive and symmetric relation R on X such that O = O_r.