Ranking intuitionistic fuzzy sets with hypervolume-based approach: An application for multi-criteria assessment of energy alternatives

Ranking Intuitionistic Fuzzy Sets (IFS) using distance-based methods involves calculating the distance between an IFS and a reference point which represents either maximum (positive ideal solution) or minimum (negative ideal solution) value. These methods assume that similarity of an IFSs to the reference point increases as its distance from it decreases. While it is a common practice to use nonlinear distance functions for ranking IFSs, this paper proves that no nonlinear IF distance function can be robust. In this study, the shortcomings of the conventional procedure are demonstrated by providing a mathematical proof and an alternative ranking method based on the hypervolume metric is proposed. In addition, the suggested ranking approach is extended as a new multi-criteria decision making method called Hypervolume-based Evaluation and Ranking Technique (HEART). HEART is applied for multi-criteria assessment of Turkey's energy alternatives. Results are compared with three distance based multi-criteria decision making methods: TOPSIS, VIKOR, and CODAS.