A Hypervolume Based Approach to Rank Intuitionistic Fuzzy Sets and Its Extension to Multi-criteria Decision Making Under Uncertainty
This addresses a misconception in fuzzy set theory and decision-making under uncertainty, offering a more reliable method for applications like energy assessment, though it is incremental as it builds on existing ranking approaches.
The paper tackles the problem of ranking intuitionistic fuzzy sets by proving that distance-based methods are flawed for non-linear functions and proposes a hypervolume-based alternative, extending it to a multi-criteria decision-making method called HVAS, which is applied to Turkey's energy alternatives and compared with three existing methods.
Ranking intuitionistic fuzzy sets with distance based ranking methods requires to calculate the distance between intuitionistic fuzzy set and a reference point which is known to have either maximum (positive ideal solution) or minimum (negative ideal solution) value. These group of approaches assume that as the distance of an intuitionistic fuzzy set to the reference point is decreases, the similarity of intuitionistic fuzzy set with that point increases. This is a misconception because an intuitionistic fuzzy set which has the shortest distance to positive ideal solution does not have to be the furthest from negative ideal solution for all circumstances when the distance function is nonlinear. This paper gives a mathematical proof of why this assumption is not valid for any of the non-linear distance functions and suggests a hypervolume based ranking approach as an alternative to distance based ranking. In addition, the suggested ranking approach is extended as a new multicriteria decision making method, HyperVolume based ASsessment (HVAS). HVAS is applied for multicriteria assessment of Turkey's energy alternatives. Results are compared with three well known distance based multicriteria decision making methods (TOPSIS, VIKOR, and CODAS).