Q-rung orthopair fuzzy Frank aggregation operators and its application in multiple attribute decision-making with unknown attribute weights

In decision-making problems, q-rung orthopair fuzzy sets are considered as a more effective tool than intuitionistic fuzzy sets and Pythagorean fuzzy sets. This article develops some aggregation operators based on Frank t-norm and t-conorm for fusing q-rung orthopair fuzzy (q-ROF) information. Then a multiple attribute decision-making (MADM) approach is introduced based on the proposed operators. The Frank operations of t-norm and t-conorm can have the advantage of good flexibility with the operational parameter. From that point of view, in this paper, we extend the ideas of Frank t-norm and t-conorm to the q-ROF environment and introduce some aggregation operators. Moreover, we illustrate the compatible properties of the proposed operators. Generally, the attribute weights are unknown in the MADM problems. The analytical hierarchy process and entropy methods are efficient tools to handle such MADM problems with unknown attribute weights. So, we present an MADM approach with unknown attribute weights under q-ROF environment using proposed operators. Then to elaborate the flexibility and validity of the proposed model, we discuss and solve a numerical problem concerned with a government project of choosing the best way of industrialization. Next, we show how the involvement of the parameters in our proposed model affects the decision-making results. Finally, to exhibit the superiority of our proposed methodology, the obtained results are compared with the existing ones.