A hybrid decision-making framework using rough mF bipolar soft environment

In this article, we present the notions of two novel hybrid multi-attribute decision-making models, namely m-polar fuzzy bipolar soft set (mFBSS, for short) model and rough mFBSS model. These mathematical models allow us to handle multipolar information under fuzziness with bipolar soft sets. We use these proposed models to handle complicated problems in which the degree of membership of an object in a given set uses m fuzzy values, to rank all the objects, and to find a suitable option. We illustrate our proposed concepts with examples. Furthermore, we investigate some useful properties, including complement, restricted union and intersection, extended union and intersection, AND and OR. We discuss two practical applications of mFBSSs and rough mFBSSs, that is, selecting a suitable employee for promotion and place for house construction, respectively. We develop efficient algorithms to solve multi-attribute decision-making problems. We also discuss a comparison analysis of the proposed approaches with some existing models.