Approximation of Indistinct Concepts

This theory on semi-equivalence relations is an important and useful tool for investigating classification, pattern recognition, polling and inference etc. Based on it, this paper presents a new framework, in which an indistinct concept, that is one with incomplete or undetermined information about the objects, can be represented approximately. Such an approximate representation will reflect deep structures of concepts which are meaningful for the system. Clearly, the work we present here is to a great extent inspired by general discussions of knowledge engineering research. The theory developed here seems to be of interest in knowledge representation and natural language processing. From the implementation point of view, this theory can be realized by various AI techniques. 0. INTRODUCTION Two major issues of knowledge engineering are representation and utilization of knowledge. Following Orlowska and Pawlak [1] , anything that can be spoken about in the subject position of a natural language sentence is an object, properties of which are fundamental elements of the knowledge of a given domain; then concepts are more complex elements of knowledge. This gives the possibilities of representing the concepts related to a given domain. To represent indistinct concepts the information about a set of the objects represented by such a concept is undetermined or incomplete in a sense, Pawlak [2] introduced the rough sets concepts defined by union of some equivalent classes of an equivalence relation. Unfortunately, in many real situations it is not sufficient to consider equivalence relation only. In fact, a lot of relations determined by the attributes of objects do not satisfy transitivity.This limits the expressive power of rough sets. The Preceding fact forced us to extend Pawlak' s works. Semi-equivalence relation theory [3] just offers one of the possible research directions in this field. The original idea of the theory was suggested by Poincare'. Wu Xuemou and his colleagues have established and developed the theory [3], [4]. In its framework, we give interior and exterior approximations of indistinct concepts respectively. Its gradual approximations defined in terms of a family of semi-equivalence relations are also given in it. Such approximate representations will reflect deep structures of concepts and improve the expressive power of Pawlak's knowledge representation system. The work we present in this paper provides a powerful tool for incomplete knowledge representation and utilization, and develops some new researches in AI, e.g. pattern recognition, automated deduction, search methods, etc. these will be discussed in …