Generalized intuitionistic fuzzy multiplicative interactive geometric operators and their application to multiple criteria decision making

In this paper, group decision making methods based on intuitionistic fuzzy multiplicative preference relations has been developed. For it, firstly some new operational laws on intuitionistic multiplicative numbers have been defined and then by using these operations some new intuitionistic fuzzy multiplicative interactive weighted geometric, intuitionistic fuzzy multiplicative interactive ordered weighted geometric and intuitionistic fuzzy multiplicative interactive hybrid weighted geometric operators have been developed. Some desirable properties of these operators, such as idempotency, boundedness, monotonicity etc., are studied in the paper. The major advantage of the proposed operators as compared to existing ones are that it consider the proper interaction between the membership and non-membership functions and proposed operators are more pessimistic than existing ones. Furthermore, these operators are applied to decision making problems in which experts provide theory preference relation by intuitionistic fuzzy multiplicative intuitionistic fuzzy environment to show the validity, practicality and effectiveness of the new approach. Finally, a systematic comparison between the existing work and the proposed work has been given.