On multi-granulation covering rough sets

Recently, much attention has been given to multi-granulation rough sets (MGRS) and different kinds of multi-granulation rough set models have been developed from various viewpoints. In this paper, we propose four types of multi-granulation covering rough set (MGCRS) models under covering approximation space, where a target concept is approximated by employing the maximal or minimal descriptors of objects in a given universe of discourse U. And then, we investigate a number of basic properties of the four types of MGCRS models, and discuss the relationships and differences among the classical MGRS model and our MGCRS models. Moreover, the conditions for two distinct MGCRS models which produce identical lower and upper approximations of a target concept in a covering approximation space are also studied. Finally, the relationships among the four types of MGCRS models are explored. We find that for any subset X c U, the lower approximations of X and the upper approximations of X under the four types of MGCRS models can construct a lattice, if we consider the binary relation of inclusion. (C) 2014 Elsevier Inc. All rights reserved.