Pythagorean fuzzy preference ranking organization method of enrichment evaluations

Recently, a new extension of fuzzy sets, Pythagorean fuzzy sets (PFS), has attracted a lot of attention from scholars in various fields of research. Due to PFS's powerfulness in modeling the imprecision of human perception in multicriteria decision-making (MCDM) problems, this paper aims to extend the classical preference ranking organization method of enrichment evaluations (PROMETHEE) into the Pythagorean fuzzy environment. The proposed method takes not only the weights related to different criteria but also the preference relations as Pythagorean fuzzy numbers, therefore providing a broader range of choices for the decision-maker to express their preferences. Five properties are put forward to regulate the designing of both intuitionistic and Pythagorean fuzzy PROMETHEE (PF-PROMETHEE) preference functions. Furthermore two illustrative examples are given to demonstrate the detailed procedure of PF-PROMETHEE, and comparisons are made to distinguish the differences among our proposed method, the classical PROMETHEE and intuitionistic PROMETHEE. The results show that PF-PROMETHEE is effective, comprehensive, and applicable to a wide range of MCDM problems.