A variable precision multigranulation rough set model and attribute reduction.

As a useful extension of rough sets, multigranulation rough sets (MGRSs) can be used to deal with a variety of complex data. Numerous significant advances have been achieved by generalizing MGRSs. However, most of the existing findings of MGRSs are sensitive to misclassification and noise in data. Furthermore, the studies of attribute reduction based on MGRSs have received little attention. To fill such gaps, this paper proposes an extended model of MGRSs named variable precision multigranulation rough sets (VPMGRSs) by introducing rough membership function and approximation parameters in variable precision rough sets (VPRSs) into the multigranulation environment. After giving some basic properties of VPMGRSs, we investigate the relationships between VPMGRSs and VPRSs, pessimistic MGRSs, and generalized MGRSs. In addition, several VPMGRSs-based attribute reductions are introduced, and it is proved that some of them are equivalent when the parameters in the model meet specific requirements. Finally, we propose a heuristic algorithm for α -lower distribution reduct and illustrate its effectiveness and efficiency by a comparative experiment on real datasets. [ABSTRACT FROM AUTHOR]