Evaluating Geothermal Energy Systems Using Spherical Fuzzy PROMETHEE

Abstract

Spherical fuzzy sets (SFSs) have been recently introduced to provide a larger preference domain for decision-makers. The preference ranking organization method of enrichment evaluation (PROMETHEE) is one of the known methods for multi-criteria decision making (MCDM). This study extends the conventional PROMETHEE into the spherical fuzzy environment. In the proposed method, both the weights of the criteria and the preference relations are SFSs. The relative degree of closeness is used to determine the preference indices. Since it is more appropriate to express the preference using linguistic terms, a linguistic preference function is used. Two examples are solved to illustrate the applicability and efficiency of the proposed method in solving MCDM problems. In the first example, the weights of the criteria and the ratings of the alternatives are SFSs. In the second example, the evaluation of the alternative energy exploitation projects, the weights of the criteria and the performance of the scenarios are crisp values. The results of the second example are compared with the results of the conventional PROMETHEE, the fuzzy PROMETHEE, the intuitionistic fuzzy PROMETHEE, and the Pythagorean fuzzy PROMETHEE.