Multi-attribute group decision-making based on bipolar n,m-rung orthopair fuzzy sets

The n,m-rung orthopair fuzzy set theory has appeared as a fresh mathematical tool for dealing with uncertainty in several fields of the real world. The n,m-rung orthopair fuzzy sets were introduced to make uncertain data from broadly applicable real-world decision-making scenarios tractable analytically. In this regard, n,m-rung orthopair fuzzy sets outperform intuitionistic, Pythagorean, Fermatean, and q-rung orthopair fuzzy sets in terms of flexibility and dependability. Bipolar fuzzy sets are useful tools for handling fuzziness and bipolarity. The bipolar n,m-rung orthopair fuzzy set (Bn,m-ROFS) model is presented in this study as a generic extension of two powerful existing models, namely the bipolar intuitionistic fuzzy set and the bipolar Pythagorean fuzzy set models. This suggested set completely reflects both quantitative and qualitative evaluations and fully exploits the n,m-rung orthopair fuzzy set. Moreover, subset, equal, complement, intersection, and union are some key characteristics of the proposed Bn,m-ROFS model that are examined along with numerical examples. Additionally, certain fundamental operations are established here, including the bipolar n,m-rung orthopair fuzzy weighted average operator and the bipolar n,m-rung orthopair fuzzy weighted geometric operator. Furthermore, a Bn,m-ROFS application is investigated to handle various multiattribute decision-making situations, such as the choice of the best manager. The suggested methodology is backed up by an algorithm. Finally, the comparison of the indicated hybrid model with a known model, such as the bipolar Pythagorean fuzzy set, is offered.