A Euclidean Approach for Ranking Intuitionistic Fuzzy Values

In the literature on Atanassov intuitionistic fuzzy sets, several methods have been proposed in order to obtain a ranking on intuitionistic fuzzy values. However, some problems may arise when working with these methods, such as the inadmissibility problem, the nonrobustness problem, the indifference problem, etc. Based on the concept of the Euclidean distance, we propose a novel approach for ranking intuitionistic fuzzy values, which addresses these problems. With the aid of its geometrical representation, we rank the intuitionistic fuzzy values in accordance with the following basic principle: The closer the intuitionistic fuzzy value is to the most favorable intuitionistic fuzzy value, the higher the ranking of the intuitionistic fuzzy value is. Moreover, we extend this approach by taking into account human cognitive bias, which reflects a decision maker's attitude toward positive or negative consequences in decision problems involving uncertainty. Finally, we generalize our approach by introducing the Minkowski distance, and show that the generalized approach also addresses the problems encountered by the existing methods.