Research On The Relationship Between Generalized Rough Set Models And Topological Structures

Rough sets theory is a mathematical tool for dealing with inharmonious, incomplete, and uncertainty knowledge. Topology is an important branch of mathematics, and it is also an important mathematical tool for studying information systems, which has been applied in many fields of mathematics. This paper is devoted to discussing the relationship between these two theories, more details are as follows:As for the relationship between rough set models based on binary relations and topological structure, in this paper, we discuss two categories of generalized rough set models:rough set models based on the element definitions and rough set models based on the granule definitions. Four types of topological structures induced by the two rough set models are discussed, and we study the relationship between rough set and these topological structures, Furthermore, the conditions of different relations inducing the same topology are discussed.As for the relationship between rough set models based on covering, in this paper, a class of topological structures in the covering rough set models are investigated. We show that the minimum set of each of these topological structure based on the second covering upper approximation operators is their base, and a partition on the universe of discourse. Then, we induce a new covering, and construct their closure operators by using rough set. Finally, we discuss the relationships between some topologies generated by some covering approximation operators and unary covering.