Topological Structure Of Generalized Approximation Spaces And R-Separated Spaces

Rough Sets Theory, based on indiscernibility relation (i.e.equivalence relation), is used to deal with the fuzzy and uncertain knowledge. Its mainly theoretic ideas, through knowledge reduction, deduce the decision-makings and classification rules of problems under the invariable premise of classification ability, which have been applied in the field of machine learning, decision-making analysis, process control, pattern recognition and data mining.Generalized approximation spaces deduced from generalized rough sets is an important space. In this paper we mainly study topological structure of generalized approximation spaces and some properties of R -seperated spaces based on binary relation.This paper is parted into three chapters.In the first chapter, we introduced the background knowledge related to the re-search.In the second chapter, we research the topological structure of generalized ap-proximation spaces by introducing the concept Rs , that is the transferring expres-sion of the reflexive relation R on domain X , involving its topological base, countability, divisibility, compactness, separability, and connectivity. Therefore, some mainly interesting results are obtained, which can be seen in Theorem 2.3.1, Theorem 2.3.10, Theorem 2.3.14.In the third chapter, we research R -seperated spaces based on binary relation and then given some properties related to it. We also discuss the relationship be-tween R -seperated spaces and compact spaces, R -seperated spaces and Lindel&o&f fspaces, thus obtaining main results seen in Theorem 3.3.5 and Theorem 3.3.6.