Uncertainty measures of roughness of knowledge and rough sets in ordered information systems

Abstract

Rough set theory has been considered as a useful tool to deal with inexact, uncertain, or vague knowledge. However, in real-world, most of information systems are based on dominance relations, called ordered information systems, in stead of the classical equivalence for various factors. So, it is necessary to find a new measure to knowledge and rough set in ordered information systems. In this paper, we address uncertainty measures of roughness of knowledge and rough sets by introducing rough entropy in ordered information systems. We prove that the rough entropy of knowledge and rough set decreases monotonously as the granularity of information becomes finer, and obtain some conclusions, which is every helpful in future research works of ordered information systems. © Springer-Verlag Berlin Heidelberg 2007.