Affiliations: [a] College of Mathematics and Statistics, Guangxi Normal University, Guilin, China
| [b] Guangxi Universities Key Lab of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, China
Correspondence:
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Corresponding author. Pei Wang, Guangxi Universities Key Lab of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, China. E-mail: peiwang130@163.com.
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.
