Coverage Reduction And Topological Research Covering Coarse Sets

Rough set theory was introduced by Pawlark in 1982 which dealing with uncertainty problems,and now has become an active branch of information sciences as a data analysis processing theory.Meanwhile it has been successfully applied in medical science,material science,management science and so on.Generalized approximation spaces(also called relation rough sets)and covering approximation spaces(also called covering rough sets)are important generalization of classical rough sets introduced by Pawlark.To study covering rough sets,searching properties of covering rough sets like the properties of topology spaces and its reduction are significant aspects.In this paper,a topology space is induced by using the covering of a covering rough set as a subbase.Then some separation axioms and compactness of a covering rough set are defined by the induced topology space and their properties and relationships are also studied.Besides,using the induced covering rough set of a relation rough set,we introduce s-compact,p-compact and bi-compact.Their relationships and invariability under rough continuous mappings are discussed.Covering reductions and covering saturation reductions of covering rough sets are also considered in this paper.It is proved that when universe U is finite,then covering reductions of(U,C)exists and there is a unique covering saturation reduction of(U,C).An effective algorithm is constructed to compute the covering saturation reduction on a finite universe.This paper consists of five chapters.In Chapter ?,we briefly introduce the development of rough set theory and the backgrounds of this thesis.Some preliminaries are also given.In chapter ?,we introduce induced relation rough sets and induced covering rough sets,give some induced methods of covering rough sets induced by relations and relation rough sets induced by coverings.In chapter ?,we introduce the definitions and descriptions of separation axioms of the covering rough set using the induced topology space.By the compactness of the induced covering rough sets,here defines s-compact,p-compact,bi-compact of generalized approximation spaces.Relationships between the three compactness andrelational compact and topological-compact are studied.At the same time,whether the five compactness still hold under rough continuous mappings is also checking.In chapter IV,for covering rough sets,the concepts of covering reductions,covering saturation reductions and core are introduced.Global properties of covering reduction and covering saturation reduction are investigated.The concept of core of a covering is also given.It is also proved that for covering rough set on a finite universe,there exists covering reductions and there is one and only one covering saturation reduction.Besides,here illustrates that the covering saturation reduction may not be a covering reduction and a covering reduction may not be the covering saturation reduction.The sufficient and necessary conditions of a covering reduction being the covering saturation reduction are given.In chapter V,we summarize our major work in this paper and propose some further possible topics in the future.