Decision making with geometric aggregation operators based on intuitionistic fuzzy sets

Abstract

Xu and Yager (2006) proposed some geometric aggregation operators based on intuitionistic fuzzy sets (IFS) and introduced the concept of sub-interval of membership values to define IFS. Based on the sub-interval, they defined various geometric aggregation operators such as intuitionistic fuzzy weighted geometric (IFWG) operator, intuitionistic fuzzy ordered weighted geometric (IFOWG) operator, and intuitionistic fuzzy hybrid geometric (IFHG) operator. In this paper, we propose these geometric aggregation operators (IFWG, IFOWG, and IFHG) based on IFS using the sub-interval of non-membership values. These operators can be used in an environment where the arguments are presented as intuitionistic fuzzy sets. Numerical examples are given to illustrate the operators. We also present an algorithm to show the application of the IFHG operator to multiple attribute decision making (MADM) problems based on intuitionistic fuzzy sets. Finally the algorithm has also been illustrated through a numerical example.