A Novel Approach for Fuzzification of Rough Sets Based on Fuzzy Preference Relation: Properties and Application to Medicine Selection Problem
Rizwan Gul, Saba Ayub, Muhammad Shabir, Ali Yahya Hummdi, Amer Aljaedi, Zaid Bassfar
Abstract
Preference analysis is a significant component in decision-making (DM) when selecting an optimal alternative. By comparing any two alternatives pairwise, preference relations (PRs) effectively depict the preference degrees of decision-makers (DMrs). The rough set theory (RST) has been effectively applied to cope with preference analysis by swapping the equivalence relation (Er) with the dominance relation (DR). In this study, we propose new transfer functions to construct alternatives’ upward/downward fuzzy preference degree (FPD) for evaluating upward and downward fuzzy PRs (FPRs). Based on these newly proposed transfer functions, we present a novel method for fuzzifying RSs called the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">upward</i> α- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fuzzified preference rough sets</i> (α↑-FPRSs). The basic properties of the proposed α↑-FPRSs are thoroughly studied. Moreover, several uncertainty measures related to α↑-FPRSs are presented. Meanwhile, we offered the notion of upward fuzzy β-covering (UFβC) and upward fuzzy β-neighborhood (UFβ-nghd), upward β-neighborhood (Uβ-nghd), and several related properties are explored. Based on UFβ-nghd and Uβ-nghd, we construct two new models of UFβC rough sets (UFβ-CRSs) along with their properties. We formulate a novel technique of multi-attribute DM (MADM). To legitimise the practicality of our proposed model, we provide a real-life example of selecting an appropriate medication to treat a specific disease. Finally, we look into the efficacy of the launched scheme through a comparison study.