On Topological Structure Of Generalized Rough Sets And Its Applications

Firstly, we discuss some properties of two pairs of generalized approximation operators, and the relations among the topologies generated by generalized approximation operators, relative operators and pseudo-closure operators. We also explore some topological properties of those topologies, such as connectedness, separation property and so on, and their applications in rough sets. Secondly, we discuss some of their applications by topological rough membership function, explore some properties of the topological rough membership function. Then based on those properties, we discuss the reduction of a covering generated by an inverse serial relation, which preserves the topological rough membership function and is characterized by the rough entropy. In particular, we introduce the relation reduction in a family of inverse serial relations, which preserves the topological rough membership function. We also give a new discernibility matrix to characterized it. And our results extend some important results on the reduction in information systems.