Multigranulation fuzzy probabilistic rough sets induced by overlap functions and their applications

As we all know, t-norms can be used to construct fuzzy probabilistic rough set (FPRS). Meanwhile, overlap functions (OFs), as a sort of novel aggregation functions different from t-norms, have shown a flourishing situation in terms of applications and theory, especially for the study involving combination of OFs with rough sets. In this paper, we propose a novel OFs-based FPRS named as OFPRS. Specifically, first, we provide a pair of approximation operators of OFPRS via the conditional probability based on OFs. Meanwhile, we present a new OFs-based multigranulation fuzzy probabilistic rough set named as OMGFPRS. Then, we study elementary properties of OFPRS and OMGFPRS. Furthermore, we list practical examples to illustrate the feasibility as well as effectiveness of OFPRS and OMGFPRS, and give a short comparison of the proposed models with existing corresponding FPRS models. Lastly, we develop numerical experiments where OFPRS and OMGFPRS have better classification performance than t-norms-based FPRS.