Abstract
Intuitionistic uncertain linguistic variables (IULVs) are useful to express the qualitative and quantitative recognitions of decision makers. However, after reviewing the previous operational laws on IULVs, we find there are some limitations. To address these issues, we define several new operations on IULVs and give a new ranking method. To improve the utilization of IULVs, this paper defines two Choquet operators: the intuitionistic uncertain linguistic symmetrical Choquet averaging (IULSCA) operator and the intuitionistic uncertain linguistic symmetrical Choquet geometric mean (IULSCGM) operator, which can address the internal correlations among elements. To globally reflect the interactive characteristics of the importance of elements, two generalized Shapley intuitionistic uncertain linguistic symmetrical Choquet operators are presented. Subsequently, a new distance measure is defined, which is then used to build models to ascertain fuzzy measures on decision maker and criteria sets to address the case where the weighting information is partly known. After that, a new procedure to intuitionistic uncertain linguistic group decision making is developed. Finally, a specific example is offered to illustrate the practicality of the new procedure, and the comparison analysis is also made.