A multigranulation rough set model based on variable precision neighborhood and its applications

As combinations of neighborhood rough sets and multigranulation rough sets (MRSs), optimistic and pessimistic neighborhood MRSs can handle complex information systems and characterize problems from multiple perspectives. Nevertheless, they require complete inclusion between neighborhood granules and target concepts, which may weaken their fault tolerance. To overcome the challenge, this paper proposes neighborhood MRSs based on variable precision neighborhood (VMRSs), which allow a certain degree of misclassification and noise in data. In VMRSs, we assign different weights to different attribute subsets to distinguish their importance in learning. In addition to investigating the properties of the VMRS model, we focus on the methods of obtaining its required multiple attribute subsets and their weights. Next, we introduce two applications of the VMRS model. One is using it to construct an indicator for evaluating attribute clustering and attribute subset weighting methods. The other is employing it for attribute reduction. Based on distribution distances, we develop a heuristic algorithm framework for obtaining the proposed reducts. The mechanism and applications of VMRSs are explained through a case study on a medical diagnosis issue. Finally, the experiments on real datasets illuminate the effectiveness and superiority of the methods and algorithms in the paper.