Covering-based $$(\alpha , \beta )$$ ( α , β ) -multi-granulation bipolar fuzzy rough set model under bipolar fuzzy preference relation with decision-making applications

Abstract

Abstract 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 $$\delta $$ δ -covering (BFP $$\delta $$ δ C), we put forward the idea of BFP $$\delta $$ δ C based optimistic multi-granulation bipolar fuzzy rough set (BFP $$\delta $$ δ C-OMG-BFRS) model and BFP $$\delta $$ δ C based pessimistic multi-granulation bipolar fuzzy rough set (BFP $$\delta $$ δ C-PMG-BFRS) model. We examine several significant structural properties of BFP $$\delta $$ δ C-OMG-BFRS and BFP $$\delta $$ δ C-PMG-BFRS models in detail. Moreover, we discuss the relationship between BFP $$\delta $$ δ C-OMG-BFRS and BFP $$\delta $$ δ C-PMG-BFRS models. Eventually, we apply the BFP $$\delta $$ δ 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.

Keywords

• Rough set
• Bipolar fuzzy preference relation
• BFP $$\delta $$ δ C-OMG-BFRS
• BFP $$\delta $$ δ C-PMG-BFRS
• MCDM