Reduction of subbases and its applications

Abstract

Based on properties of the topological rough membership function, we discuss the reduction of a subbase for a topology, which preserves the topological rough membership function and is characterized by the rough entropy. Furthermore, we introduce the subbase reduction in a family of subbases, which preserves the topological rough membership function. We also give a discernibility matrix to characterized it. As applications, our results extend some important results on the reduction in information systems.