A comprehensive study on $(\alpha , \beta )$-bipolar fuzzified rough set model based on bipolar fuzzy preference relation and corresponding decision-making applications

Abstract

Preference analysis is an essential component of the decision-making (DM) process for identifying the optimal object. The rough set (RS) theory has 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 article, we first established the idea of bipolar fuzzy preference relation (BFPR) from the bipolar fuzzy information system and studied some of its basic properties. Then, based on BFPR, a novel idea of $(\alpha , \beta )$-bipolar fuzzified preference RSs ($(\alpha , \beta )$-BFPRSs) is offered. Several significant structural properties of $(\alpha , \beta )$-BFPRSs are analyzed in detail. Moreover, some significant uncertainty measures associated with $(\alpha , \beta )$-BFPRSs are proposed. Meanwhile, we put forward the idea of bipolar fuzzy preference $\delta$-covering ($BFP\delta C$), bipolar fuzzy preference $\delta$-neighborhood (BFP$\delta$-nghd), and bipolar preference $\delta$-neighborhood (BP$\delta$-nghd). Moreover, we establish a new type of bipolar fuzzy RS (BFRS) model in the context of BFP$\delta$-nghd, and several relevant properties are explored. Using the theory of the $BFP\delta C$-based BFRS model, we develop a novel approach for multi-criteria decision-making (MCDM) problem. A real-life example of a smartphone selection is provided to show the applicability of our suggested approach. We further investigate the effectiveness of the developed technique using a comparative analysis. Last but not least, theoretical investigations and practical examples reveal that our suggested approach dramatically enriches the RS theory and offers a novel knowledge discovery strategy that is applicable in real-world circumstances.