Generalized intuitionistic fuzzy geometric interaction operators and their application to decision making

• New operational laws on intuitionistic fuzzy sets are presented.
• A series of new generalized intuitionistic fuzzy aggregation operators are developed.
• The properties of the new generalized aggregation operators are investigated.
• We apply the proposed approach to multiple attributes decision making.
• We give a systematic comparison between this paper and other papers.

Considering that there may exist some interactions between membership function and non-membership function of different intuitionistic fuzzy sets, we present some new operational laws from the probability point of view and give a geometric interpretation of the new operations. Based on which, a new class of generalized intuitionistic fuzzy aggregation operators are developed, including the generalized intuitionistic fuzzy weighted geometric interaction averaging (GIFWGIA) operator, the generalized intuitionistic fuzzy ordered weighted geometric interaction averaging (GIFOWGIA) operator and the generalized intuitionistic fuzzy hybrid geometric interaction averaging (GIFHGIA) operator. The properties of these new generalized aggregation operators are investigated. Moreover, approaches to multiple attributes decision making are given based on the generalized aggregation operators under intuitionistic fuzzy environment, and an example is illustrated to show the validity and feasibility of new approach. Finally, we give a systematic comparison between the work of this paper and that of other papers.