Covering numbers in covering-based rough sets

Abstract

Rough set theory provides a systematic way for rule extraction, attribute reduction and knowledge classification in information systems. Some measurements are important in rough sets. For example, information entropy, knowledge dependency are useful in attribute reduction algorithms. This paper proposes the concepts of the lower and upper covering numbers to establish measurements in covering-based rough sets which are generalizations of rough sets. With covering numbers, we establish a distance structure, two semilattices and a lattice for covering-based rough sets. The new concepts are helpful in studying covering-based rough sets from topological and algebraical viewpoints. © 2011 Springer-Verlag.