A Novel Approach Toward Roughness of Bipolar Soft Sets and Their Applications in MCGDM

The uncertainty in the data is an obstacle in decision-making (DM) problems. In order to solve problems with a variety of uncertainties a number of useful mathematical approaches together with fuzzy sets, rough sets, soft sets, bipolar soft sets have been developed. The rough set theory is an effective technique to study the uncertainty in data, while bipolar soft sets have the ability to handle the vagueness, as well as bipolarity of the data in a variety of situations. This study develops a new methodology, which we call the theory of dominance-based bipolar soft rough sets (DB-BSRSs), which will be used to propose a new technique to solve decision-making problems. The idea introduced in this study has never been discussed earlier. Furthermore, this concept has been explored by means of a detailed study of the structural properties. Moreover, some important measures like the accuracy measure, the measure of precision, and the measure of quality for DB-BSRSs are also provided. Finally, an application of the DB-BSRSs in multi-criteria group decision-making (MCGDM) problem is presented and an algorithm for this application is proposed, supported by an example, which yields the best decision, as well as, the worst decision between some objects. In comparison with some existing results, we also present some advantages of our proposed method.