Study on open operation and compactness based on constructing rough set L-f topological space

Abstract

How to construct topological space in rough set and study its topological space open operation and compactness was presented. The rough set topological space was constructed by using the equivalence class and the rough set L – f topological space was constructed by using mapping, which is first established. To obtain the essential attributes of the constructed rough set L – f topological space, the following five techniques were used: the opening operation of the L – f topological space can be defined by using the inductive method, and it was proved that the L – f topological space by using deductive reasoning which satisfied the β – open operation, the correctness and open coverage of the topological space can be defined by using the set, and it was proved that the L – f topological space was β – correctness by using deductive reasoning at the same time. Furthermore, it was verified that the constructed rough set L – f topological space by using data was very effective. The theoretical results had important significance in the promote study the topological space of rough set.