A Novel Scheme of Roughness of Soft Sets Under Soft Binary Relations and Its Applications in Decision Analysis

Binary relations are crucial in the domains of information sciences and mathematics. In real-world scenarios, rough sets (RS) and soft sets (SS) are remarkable mathematical paradigms for handling imprecise and ambiguous data. This paper presents an innovative approach to the roughness of the SS regarding foresets (F-sets) and aftersets (A-sets), using soft binary relations (SBRs), which offer a more flexible method than existing techniques by extending the scope of applications through a reliance on a general SBR without constraints. First, two pairs of SSs are established by adopting an SBR to approximate a soft subset, and their unique axiomatic systems are analyzed. Two varieties of soft topologies derived from soft reflexive relations (SRRs) are also inspected. Besides, several similarity relations associated with SBRS are also explored. We next devise a decision-making methodology within the environment of the endorsed approach. In addition, we provide the two decision-making algorithms. Eventually, an applied example is implemented to evaluate the reliability and practicality of the decision processes. An extensive comparison study confirms the projected method’s feasibility and superiority over existing approaches to decision-making.