Knowledge spaces and reduction of covering approximation spaces

Abstract

Theory of covering rough sets is one kind of effective methods for knowledge discovery. In Bonikowski covering approximation spaces, all definable sets on the universe form a knowledge space. This paper focuses on the theoretic study of knowledge spaces of covering approximation spaces. One kind of dependence relations among covering approximation spaces is introduced, the relationship between the dependence relation and lower and upper covering approximation operators are discussed in detail, and knowledge spaces of covering approximation spaces are well characterized by them. By exploring the dependence relation between a covering approximation space and its sub-spaces, the notion of the reduction of covering approximation spaces is induced, and the properties of the reductions are investigated.