A Novel Constructing Continuous and Topology Approach to Fuzzy β-covering

Abstract

Fuzzy β-covering(Fβ-C) plays a key role in processing real-valued data sets and covering plays an important role in the topological spaces. Thus they have attracted much attention. But the relationship between Fβ-C and topology has not been studied. This inspires the research of Fβ-C from the perspective of topology. In this paper, we construct Fβ-C rough continuous and homeomorphism mappings by using Fβ-C operator. We not only obtain some equivalent descriptions of the mappings but also profoundly reveal the relationship of two Fβ-C approximation spaces. We give the classification method of Fβ-C approximation spaces with the help of homeomorphism mapping, propose a new method to construct topology induced by Fβ-C operator and investigate the properties in the topological spaces further. Finally, we obtain the necessary and sufficient conditions for Fβ-C operators to be topological closure operators.