Roughness of fuzzy sets by binary relations induced from soft relations with application in decision making

Abstract

Binary relations are significant in mathematics and information sciences. Meanwhile, fuzzy set (FS), rough set (RSs) and soft set (SS) are efficient mathematical schemes for dealing with uncertain and vague information in real-world circumstances. This article explores rough approximations of a FS based on induced binary relations from a soft relation that are given in terms of foresets and aftersets. Initially, two pairs of rough approximations founded on induced binary relations are analyzed, and their distinctive features are reviewed. In addition, two variants of fuzzy topologies are constructed by induced reflexive relations. Meanwhile, several similarity relations associated with induced reflexive relations are also discussed. Also, we outline a method to decision-making (DM) within the invented approach. The decision steps and the algorithms of the decision method are also specified. The legitimacy of the decision method is verified by a practical illustration. A detailed comparative analysis further authenticates the viability and efficacy of the projected method over existing decision-making techniques.