q-Rung orthopair fuzzy uncertain linguistic choquet integral operators and their application to multi-attribute decision making

Multiple attribute decision making (MADM) problems widely exist in real decision making, and MADM methods with linguistic information have achieved great success. However, as the complexity of decision making problems is increasing in the real world, it is of great necessity to further develop new expression of evaluation information and aggregation technologies that can reflect the correlation among multi-attributes under uncertain decision-making environment. In response, this paper originally presents q-rung orthopair fuzzy uncertain linguistic set (q-ROULS) by combining q-rung orthopair fuzzy set (q-ROFS) and uncertain linguistic set (ULS). Then operational laws, expected functions and accuracy functions of q-rung orthopair uncertain linguistic variables (q-ROULVs) are also defined. Considering the correlation between q-ROULVs, we propose a family of q-rung orthopair fuzzy uncertain linguistic Choquet integral operators to aggregate q-rung orthopair uncertain linguistic information. Further, a novel MADM technique is presented based on the proposed q-rung orthopair fuzzy uncertain linguistic Choquet integral operators. The developed MADM method with q-rung orthopair fuzzy uncertain linguistic information enriches fuzzy decision-making theory and provides a new way for decision makers (DMs) under q-rung orthopair fuzzy uncertain linguistic environment.