Topological Research Of Generalized Approximate Space And Multiple Reductions Of Abstract Knowledge Base

In 1982,Z.Pawlark introduced rough set theory for dealing with inaccuracy,uncertainty and incomplete data.In recent years,the theory is widely used in machine learning,knowledge discovery,data mining,decision-making and analysis.Later on,people introduced generalized approximation spaces and abstract knowledge bases which are generalizations from core concepts of rough set theory.The study of these new theories has great theoretical significance and application value.For generalized approximation spaces,we study them from topological point of view.Firstly,we propose relational topologies formed by relational open sets of generalized approximation spaces.We define some separation axioms and topological compactness of generalized approximation spaces in terms of relational topologies and obtain results about these separation axioms.We also prove that relational compactness is stronger than topological compactness of generalized approximation spaces.Secondly,rough continuity and topological continuity of maps between generalized approximation spaces are introduced and their properties are explored.It is proved that every rough continuous map is topological continuous.With these two continuities,concepts of rough homeomorphism properties and topological homeomorphism properties are defined.We investigate some properties such as separation axioms,connectedness and compactness of generalized approximation spaces whether they are rough(topological)homeomorphism properties.It is proved that every topological homeomorphism property is a rough homeomorphism property.At last,it is shown that generalized approximation spaces as objects and rough continuous maps as morphisms can form a category,called the category of generalized approximation spaces.We also define relational product spaces by binary relations of generalized approximation spaces and discuss some finite multiplicative properties of generalized approximation spaces.It is proved that the relational product is equivalent to the category product in the category of generalized approximation spaces.These enrich generalized approximation space theory,and provide some new ways and methods for studying and distinguishing generalized approximation spaces.For abstract knowledge bases,this paper proposes new concepts of reductions and studies them deeply.First of all,we define the discemibility matrix of an abstract knowledge base and get a method to calculate cores of abstract knowledge bases.Secondly,the concepts of join reductions and join saturation reductions of abstract knowledge bases are introduced.We also discuss relationships between join reductions and join saturation reductions under certain conditions.It is proved that for an abstract knowledge base on finite universe,there exists a unique join saturation reduction and an algorithm for obtaining this reduction is given.Finally,some examples and properties of knowledge bases are explored,and simple applications are given.This paper consists of five chapters.In Chapter ?,we briefly introduce backgrounds and preliminaries.In Chapter ?,relational topologies,separation axioms and compactness of generalized approximation spaces are introduced.In Chapter ?,we introduce rough continuity and rough homeomorphism properties of maps.In Chapter ?,relational product spaces and the category of generalized approximation spaces are introduced and investigated.In Chapter ?,we study join saturation reductions of abstact knowledge bases and give a relevant algorithm and simple applications.