Choquet-Frank aggregation operators based on q-rung orthopair fuzzy settings and their application in multi-attribute decision making

The main theory of intuitionistic and Pythagorean fuzzy sets was modified by Yager in (IEEE Trans Fuzzy Syst 25: 1222-1230, 2016) to pioneer the valuable and fundamental theory of q-rung orthopair fuzzy set (QROFS), which is expressed to be massive reliable, and dominant to evaluate awkward and complex information in a practical decision-making scenario. Furthermore, frank t-norm and t-conorm are also very important and valuable in the field of fuzzy set theory. The main evaluation of this analysis is to develop certain dominant operational laws under the consideration of frank t-norm and t-conorm. Moreover, to investigate the relationships among any number of attributes, the Choquet-Frank operator is the massive dominant technique to elaborate on the consistency and partibility of the initiated works. Keeping the supremacy of the Choquet-Frank operators, the technique of q-rung orthopair fuzzy Choquet-Frank averaging (QROFCFA) operator, q-rung orthopair fuzzy Choquet-Frank geometric (QROFCFG) operator, and their important properties are also elaborated. These operators are more modified and generalized than the existing and simple averaging\geometric aggregation operators. Additionally, MADM (“multi-attribute decision-making”) performance is used for evaluating the beneficial and valuable decisions from the family of decisions. The main influence of this technique is to develop it under the consideration of pioneered operators to enhance the worth and capacity of the established information. Finally, to expose the effectiveness and dominancy of the initiated works, we discuss the advantages, sensitive analysis, and geometrical exposure of the explored works with the help of numerous examples.