RETRACTION:A novel approach to multi-attribute group decision-making based on q-rung orthopair fuzzy power dual Muirhead mean operators and novel score function

The recently proposed q-rung orthopair fuzzy sets (q-ROFSs) have been proved to be an effective tool to describe decision makers' evaluation information and this paper attempts to propose a new multi-attribute group decision-making (MAGDM) method with q-rung orthopair fuzzy information. First of all, we propose a new score function of q-rung orthopair fuzzy numbers (q-ROFNs) by taking the hesitancy degree into account. When considering to fuse q-ROFNs, this paper tries to propose some novel aggregation operators. The power geometric (PG) operator has the ability of reducing or eliminating the bad influence of decision makers' unreasonable assessments on final decision results. Hence, we extend PG to q-ROFSs and propose the q-ROF power geometric operator and its weighted form. The most prominent advantage of dual Muirhead mean (DMM) is that it can capture the interrelationships among any numbers of input arguments. To take full advantages of PG and DMM, we further combine PG with DMM within q-rung orthopair fuzzy environment and propose the q-rung orthopair fuzzy power dual Muirhead mean, and q-rung orthopair fuzzy weighted power dual Muirhead mean operators. The proposed operators can reduce the negative effects of unreasonable evaluations on the decision results, and simultaneously take the interrelationship among any numbers of input arguments into account. In addition, we propose a new MAGDM method based on the proposed aggregation operators. Finally, we provide numerical examples to demonstrate the validity and merits of the proposed method.