Covering-based(,)-multi-granulation bipolar fuzzy rough setmodel under bipolar fuzzy preference relation with decision-makingapplications

The rough set (RS) and multi-granulation rough set (MGRS) theories have been successfully extended to accommodate preference analysis by substituting the equivalence relation (ER) with the dominance relation (DR). On the other hand, bipolarity refers to the explicit handling of positive and negative aspects of data. In this paper, with the help of bipolar fuzzy preference relation (BFPR) and bipolar fuzzy preference delta-covering (BFP delta C), we put forward the idea of BFP delta C based optimistic multi-granulation bipolar fuzzy rough set (BFP delta C-OMG-BFRS) model and BFP delta C based pessimistic multi-granulation bipolar fuzzy rough set (BFP delta C-PMG-BFRS) model. We examine several significant structural properties of BFP delta C-OMG-BFRS and BFP delta C-PMG-BFRS models in detail. Moreover, we discuss the relationship between BFP delta C-OMG-BFRS and BFP delta C-PMG-BFRS models. Eventually, we apply the BFP delta C-OMG-BFRS model for solving multi-criteria decision-making (MCDM). Furthermore, we demonstrate the effectiveness and feasibility of our designed approach by solving a numerical example. We further conduct a detailed comparison with certain existing methods. Last but not least, theoretical studies and practical examples reveals that our suggested approach dramatically enriches the MGRS theory and offers a novel strategy for knowledge discovery, which is practical in real-world circumstances.