Applied Mathematics & Information Sciences

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Recently, a multigranulation rough set (MGRS) has become a new direction in rough set theory, which is different from the Pawlake’s rough set since the former takes multiple granulations on the universe into account. In this paper, by analyzing the limitations of optimistic multigranulation rough set (OMGRS) and pessimistic multigranulation rough set (PMGRS) in incomplete information system, the incomplete variable multigranulation rough set (VMGRS) is proposed, and the relationships among VMGRS, OMGRS and PMGRS are deeply explored, From the properties, it can be found that OMGRS and PMGRS are the special cases compared to our VMGRS. Furthermore, several important measurements are introduced into the VMGRS; it is shown that the measurements of the VMGRS are between the measurements of OMGRS and PMGRS. Finally, some numerical examples are employed to substantiate the conceptual arguments.

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