Incomplete Multigranulation Rough Sets in Incomplete Ordered Decision System

The tolerance relation based incomplete multigranulation rough set is not able to explore the incomplete ordered decision systems. To solve such problem, similarity dominance relation based rough set approach is introduced into multigranulation environment in this paper. Two different types of models: similarity dominance relation based optimistic incomplete multigranulation rough set model and pessimistic incomplete multigranulation rough set model are constructed respectively. The properties and the relationships of them are discussed. Eight types of decision rules in the two models are proposed. An illustrative example is employed.