Multigranulation soft rough sets

Abstract

The classical soft rough set theory offers a formal theoretical framework for solving the uncertainty under a single granulation environment. However, it is noticeable that the soft rough set theory cannot be applied in the situation of multigranulation in the real world. To address this issue, in this paper we firstly present two types of multigranulation soft rough sets, which are the optimistic multigranulation soft rough set and the pessimistic multigranulation soft rough set. Then the basic and important properties of these multigranulation soft rough sets are studied. Finally, we investigate the relationships among single granulation soft rough set, namely classical soft rough set, optimistic multigranulation soft rough set and pessimistic multigranulation soft rough set. These results will enrich the soft set theory and multigranulation rough set theory, and also extend their application scopes.