A comparison of two types of rough sets induced by coverings

Rough set theory is an important technique in knowledge discovery in databases. in covering-based rough sets, many types of rough set models were established in recent years. In this paper, we compare the covering-based rough sets defined by Zhu with ones defined by Xu and Zhang. We further explore the properties and structures of these types of rough set models. We also consider the reduction of coverings. Finally, the axiomatic systems for the lower and upper approximations defined by Xu and Zhang are constructed. (C) 2008 Elsevier Inc. All rights reserved.