Multi-attribute Group Decision Making Method with Unknown Attribute Weights Based on the Q-rung Orthopair Uncertain Linguistic Power Muirhead Mean Operators

Q-rung orthopair uncertain linguistic sets (q-ROULSs) are a powerful tool for describing ambiguity and uncertainty of linguistic information. In this study, considering that in most multi-attribute group decision making (MAGDM) problems, not only the quantitative evaluation information of decision makers but also the qualitative evaluation opinions should be considered. Therefore, we develop a novel MAGDM method with unknown attribute weights under the q-rung orthopair uncertain linguistic environments. We firstly propose the cross-entropy of q-ROULSs, which is utilized to solve the optimal attribute weights by a linear programming model. In order to effectively summarize the unclear language information of q-ROULSs, we extend the power Muirhead mean (PMM) operator to q-ROULSs, and propose a family of q-rung othpair uncertain linguistic power Muirhead mean (q-ROULPMM) operators. The advantage of the PMM operator is that it not only mitigates the adverse effects of too high or too low attribute values on the results, but also takes into account the interrelationships between attribute values. At the same time, some ideal properties and special cases of the q-ROULPMM operator are also studied. Further, a new method based on the proposed cross-entropy and aggregation operators is developed for solving the MAGDM problem under q-ROULSs. Finally, we carried out numerical experiments to prove the effectiveness and superiority of the method.