Linguistic intuitionistic fuzzy Hamacher aggregation operators and their application to group decision making

Linguistic intuitionistic fuzzy variables (LIFVs) can efficiently denote the qualitative preferred and non-preferred cognitions of decision makers. This paper researches group decision making with linguistic intuitionistic fuzzy information. To do this, several Hamacher operational laws on LIFVs are defined. To derive the comprehensive evaluating values of alternatives, several linguistic intuitionistic fuzzy Hamacher aggregation operators are proposed, including the linguistic intuitionistic fuzzy Hamacher weighted average operator, the linguistic intuitionistic fuzzy Hamacher weighted geometric mean operator, the linguistic intuitionistic fuzzy Hamacher ordered weighted average operator, the linguistic intuitionistic fuzzy Hamacher ordered weighted geometric mean operator, the linguistic intuitionistic fuzzy Hamacher hybrid weighted average operator, and the linguistic intuitionistic fuzzy Hamacher hybrid weighted geometric mean operator. Then, several of their desirable properties are researched to guarantee the rationality. Methods for determining the weights of criteria, decision makers as well as the ordered positions are offered, respectively. After that, a procedure for group decision making with linguistic intuitionistic fuzzy information is provided. Finally, a group decision-making problem is offered to illustrate the application of the new results.