Multi-Attribute Decision-Making Based on Picture Fuzzy Einstein Operator and The TOPSIS Method

Abstract

Picture Fuzzy Sets (PFSs) denote the extension of conventional fuzzy sets, which capture a broader spectrum of human opinions, encompassing responses such as acceptance, neutrality, rejection, and hesitation. This wider range of responses cannot be accurately accommodated within fuzzy sets as well as intuitionistic fuzzy sets framework. In the realm of Multiple Attribute Group Decision-Making (MAGDM) methods, attributes frequently exhibit conflicts, uncertainties, imprecisions, as well as a lack of commensurability. To tackle the complexities inherent in MAGDM, the Technique for Order of Preference by Similarity to the Ideal Solution (TOPSIS) method has demonstrated its effectiveness. This method is employed in a compromise ranking approach founded on aggregation functions that showcase closeness to the reference points. This study's goal is to instigate a fresh approach to aggregation, referred to as the Picture Fuzzy Einstein Weighted Averaging Distance-based TOPSIS (PFEWAD-TOPSIS) method. To validate the effectiveness of this method in addressing MAGDM problems, a detailed example is conducted.