Some intuitionistic uncertain linguistic Bonferroni mean operators and their application to group decision making

With respect to multi-attribute group decision-making (MAGDM) problems in which the attribute values take the form of intuitionistic uncertain linguistic variables (IULVs), the group decision-making methods based on some Bonferroni mean (BM) aggregation operators were developed. Firstly, we proposed some new operational rules for the IULVs which can overcome the weaknesses of the existing operations. Then, we extended BM operator to the IULVs and developed intuitionistic uncertain linguistic arithmetic Bonferroni mean (IULABM) operator, intuitionistic uncertain linguistic arithmetic weighted Bonferroni mean (IULWABM) operator, intuitionistic uncertain linguistic geometric Bonferroni mean (IULGBM) operator, and intuitionistic uncertain linguistic weighted geometric Bonferroni mean (IULWGBM) operator. At the same time, some desirable properties of the proposed operators, such as idempotency, boundedness, and monotonicity, were studied, and some special cases of these operators were analyzed. Moreover, some approaches based on the developed operators are proposed. Finally, an illustrative example is given to show the steps of the developed methods and to discuss the influences of different parameters on the decision-making results.