Two-Phase Group Decision-Aiding System using ELECTRE III Method in Pythagorean Fuzzy Environment

This paper is in the continuation of a well-established line of research in multi-criteria decision making, namely, the development of the basic ELECTRE methodology. In the present study, we make an attempt to enhance the influence of the ELECTRE III method, which was conceived in response to the deficiency that existing variants of the ELECTRE method did not provide a full ordering of the alternatives. ELECTRE III has been recently extended so as to make use of information in the form of intuitionistic fuzzy sets. Although this enhancement has been acclaimed by many scholars, it is nonetheless true that further progresses can be made in the quest of generality. In this research, we develop a two-phase Pythagorean fuzzy version of standard ELECTRE III method, called two-phase Pythagorean fuzzy ELECTRE III (PF-ELECTRE III) approach. It takes full advantage of the capabilities of Pythagorean fuzzy sets (PFS); a successful model that generalizes intuitionistic fuzzy sets in a practical and intuitive way. The group decision support system of PF-ELECTRE III first evaluates the performances of the alternatives characterized by Pythagorean fuzzy numbers. The second stage produces a complete ranking of the alternatives from their evaluations in the first phase. We formulate the approach by defining PF indifference threshold, preference threshold and veto threshold functions which provide a more reliable basis to construct outranking relations. The ranking module of the PF-ELECTRE III method is simplified by computing the concordance credibility, discordance credibility and net credibility degrees of each alternative. A diagrammatic representation of the group decision-supporting system is presented to justify the corresponding step-by-step approach for solving problems. Finally, the haze management problem is solved to verify the applicability of the approach proposed in this paper. The investigation of this model and its performance paves the way to additional generalizations by other models like q -rung orthopair fuzzy sets.