Several Reductions Of Abstract Knowledge Base And Their Relations

Rough set theory is a new mathematics tool for dealing with fuzzyness and uncertainty of knowledge, 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. In rough set theory, knowledge reductions and generatings are important research topics and criti-cal steps of knowledge acquisition.This paper consists of five chapters.In Chapter I, we briefly introduce the development of rough set theory and the backgrounds of this thesis. Some preliminaries are also given.In chapter Ⅱ, for a universe U, we propose the concept of meet-generating of knowledge. We also study properties of meet-generating of knowledge. It is proved that when U is a finite universe and a given family of sets on U which is closed w.r.t unions, then the meet-generating of the family forms a topology on U. A counterexample is constructed to show that if U is infinite, then the meet-generating of a family needn’t be a topology generally. An effective algorism is given to compute the meet-generating of a family on a finite universe. It is proved that the algorism indeed computes the meet-generating.In chapter III, we generalize knowledge bases to abstract knowledge bases, give the concept of finite reductions and study (abstract) knowledge bases on infinite universe by considering the problem of existence of finite reductions of infinite knowledge bases. Some sufficient and/or necessary conditions for existence of finite reductions of an infinite abstract knowledge base are given by using of the saturation of an abstract knowledge base. Some examples are constructed to reveal various cases of existence of knowledge reductions.In chapter IV, for abstract knowledge bases, the concept of saturations and saturation reductions are introduced. Global properties of saturations and saturation reductions of abstract knowledge bases are investigated. It is proved that for an abstract knowledge base on a finite universe, there is one and only one saturation reduction. An effective algorism is constructed to compute the saturation reduction on a finite universe. We also study the restrict of saturation reductions. Simple applications of saturation reductions are also given.In Chapter V, we study transfer of knowledge reductions and attribute reductions, as well as their equivalence. It is proved that the two kinds reductions can mutually transferred and are equivalent in some sense.