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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 an FS based on induced binary relations from a soft relation that are given in terms of foresets and aftersets. We first analyze two pairs of rough approximations based on induced binary relations and review their distinctive features. Additionally, we construct two variants of fuzzy topologies through the use of induced reflexive relations. Meanwhile, several similarity relations associated with induced reflexive relations are also discussed. Moreover, we introduce a decision making (DM) method that aligns with the invented approach. The decision steps and the algorithm of the decision method are also specified. A practical illustration verifies the legitimacy of the decision method. A detailed comparative analysis further authenticates the viability and efficacy of the projected method over existing decision-making techniques. A detailed comparative analysis further authenticates the viability and efficacy of the projected method over existing decision-making techniques.
Mehmood et al. (Mon,) studied this question.