On Granularity in Information Systems Based on Binary Relation

Weihua Xu,Xiaoyan Zhang,Shihu Liu,Wenxiu Zhang

doi:10.4236/iim.2011.33010

Abstract

In this paper, some important issues of granularity are discussed mainly in information systems (ISs) based on binary relation. Firstly, the vector representation method of knowledge granules is proposed in an infor-mation system based on binary relation to eliminate limitations of set representation method. Secondly, operators among knowledge granularity are introduced and some important properties of them are studied carefully. Thirdly, distance between two knowledge granules is established and granular space is constructed based on it. Fourthly, axiomatic definition of knowledge granularity is investigated, and one can find that some existed knowledge granularities are special cases under the definition. In addition, as an application of knowledge granular space, an example is employed to validate some results in our work.

Highlights

Rough set theory, proposed by Pawlak in the early 1980s [16], is an extension of the classical set theory and can be regarded as a soft computing tool to deal with uncertainty or imprecise information
Definition 5.4([24]) Let I U, A,V, f be an information system based on binary relation and KB GS Rough entropy of knowledge granule KB, which is denoted by EKr B, can be defined as
Rough set theory is a powerful soft computing tool to deal with uncertainty and imprecision information

Summary

Introduction

Rough set theory, proposed by Pawlak in the early 1980s [16], is an extension of the classical set theory and can be regarded as a soft computing tool to deal with uncertainty or imprecise information. It was well known that this theory is based upon the classification mechanism, in which case the classification can be viewed as an equivalence relation and knowledge granules induced by the equivalence relation can be viewed as a partition of universe For this reason, it has been applied widely and successfully in feature selection [22], uncertainty reasoning [6], granular computing [9,14,29,30,31,32,33], date analysis [15,17,18] and data mining [24,25,26,27], etc.

Preliminaries

Operators among Knowledge Granules

U1p ui U

Knowledge Granularity

Case Study

Conclusions