Multi-attribute group decision-making based on intuitionistic fuzzy aggregation operators defined by weighted geometric means

This paper proposes a multi-attribute group decision-making methodology that takes advantage of a new weighted geometric mean aggregation operator on intuitionistic fuzzy numbers (IFNs). To this purpose, first, we define the intuitionistic fuzzy direct weighted geometric operator on IFNs, then we prove that it is a representable intuitionistic aggregation operator, and afterwards, we compare it with other aggregation operators motivated by the geometric mean. We use two proxies for the quantitative comparison of performances, namely the average of the Euclidean distances to the IFNs and the sum of squared error inspired by the k-means clustering algorithm.