An MCDM approach based on some new Pythagorean cubic fuzzy Frank Muirhead mean operators

Abstract

Pythagorean cubic fuzzy sets (PCFSs) are the most convenient aid to depict ambiguous data in practical decision-making situations. The Muirhead mean (MM) possesses the ability to capture the interrelationship between the criteria. Further, the MM generalizes several significant operators, for instance, the Bonferroni mean (BM) and the Maclaurin symmetric mean (MSM), etc. The Frank triangular norms can offer significant adaptability and robustness due to the presence of an additional parameter as compared to other families of triangular norms. Therefore, Muirhead mean and Frank operations can be combined for obtaining suitable results during decision-making under Pythagorean cubic fuzzy information with interrelated criteria. The primary goal of this study is to introduce some new MM operators based on Frank operations, namely, PCFFMM and PCFFGMM. Then some of the properties of PCFFMM and PCFFGMM are described. Moreover, an MCDM approach is formulated using PCFFMM and PCFFGMM operators. Eventually, the projected MCDM approach is demonstrated with a numerical example. The phenomenon of interrelationships among criteria of real-life problems can be suitably handled by the PCFFMM and PCFFGMM. The overall ranking result obtained by utilizing the proposed operators PCFFMM or PCFFGMM is more appropriate as compared to the ones obtained by using the BM, MSM, Heronian mean (HM), Choquet integral (CI), etc. Moreover, PCFFMM or PCFFGMM can be preferred ahead of BM, MSM, HM, and CI due to its computation simplicity, accuracy, flexibility, and robustness during the aggregation process of multiple correlated input data.