Information Measures of Roughness of Knowledge and Rough Sets for Incomplete Information Systems

1 IntroductionRough set thcory, introduced by Pawlak lj, is a relatively new soft computing tool todeal with vagueness and uncertainty. It has been applied to many areas successfullylncluding machine learning, data analysis, pattern recognition, decision support, datamining, process control and predictive modeling 1--6j.Rough set theory gives a formal definition of knowlcdge and provides a series of toolsto deal with know1cdge by set a1gebra. In rough set theory, know1edge can be regarded a…

Information Measures of Roughness of Knowledge and Rough Sets for Incomplete Information Systems

In this paper we address information measures of roughness of knowledge and rough sets for incomplete information systems. The definition of rough entropy of knowledge and its important properties are given. In particular, the relationship between rough entropy of knowledge and the Hartley measure of uncertainty is established. We show that rough entropy of know1edge decreases monotonously as granularity of information become smaller. This gives an information interpretation for roughness of knowledge. Based on rough entropy of knowledge and roughness of rough set. a definition of rough entropy of rough set is proposed, and we show that rough entropy of rough set decreases monotonousIy as granularity of information become smaller. This gives more accurate measure for roughness of rough set.