Intuitionistic fuzzy muirhead means motivated by frank triangular norms

The Muirhead Mean (MM) tools are more powerful and well-known operators utilized to express interrelationships among any input arguments considering different variables. Multi-attribute decision-making (MADM) technique is used to evaluate a reliable optimal option based on some realistic characteristics or criteria. The aggregation operators (AOs) play a crucial role in the aggregating and decision-making (DM) processes. In this article, we generalize the theory of intuitionistic fuzzy sets (IFSs) with Frank t-norm and t-conorm. Some robust operational laws of Frank t-norms and t-conorms are also expressed. By inspiring the significance and advantages of the MM operators, we derive some robust mathematical approaches, including intuitionistic fuzzy Frank Muirhead mean (IFFMM) and intuitionistic fuzzy Frank weighted Muirhead mean (IFFWMM) operators. By generalizing the concepts of Dual MM (DMM) operators, we establish a list of new methodologies such as intuitionistic fuzzy Frank Dual Muirhead mean (IFFDMM) and intuitionistic fuzzy Frank weighted Dual Muirhead mean (IFFWDMM). Some prominent characteristics and exceptional cases are discussed in detail. Furthermore, an algorithm is established to evaluate a MADM problem based on derived mathematical approaches. To examine the credibility and effectiveness of diagnosed approaches, we illustrate an experimental case study to assess a suitable optimal option from a group of options. To show the intensity and effectiveness of our derived approaches, a brief discussion about a comparative study is also presented, in which we compare the results of existing approaches with diagnosed mathematical approaches.