On multigranulation rough sets in incomplete information system

Multigranulation rough set is a new and interesting topic in the theory of rough set. In this paper, the multigranulation rough sets approach is introduced into the incomplete information system. The tolerance relation, the similarity relation and the limited tolerance relations are employed to construct the optimistic and the pessimistic multigranulation rough sets, respectively. Not only the properties about these multigranulation rough sets are discussed, but also the relationships among these multigranulation rough sets models are explored. It is shown that by the multigranulation rough sets theory, the limited tolerance relations based multigranulation lower approximations fall between the tolerance and the similarity relations based multigranulation lower approximations, the limited tolerance relations based multigranulation upper approximations fall between the similarity and the tolerance relations based multigranulation upper approximations. Such results are consistent to those in single-granulation based rough sets models.