A Novel PROMETHEE-Based Outranking Approach for Multiple Criteria Decision Analysis with Pythagorean Fuzzy Information

This paper aims to present a novel outranking approach of the preference ranking organization method for enrichment evaluations (PROMETHEEs) based on Pythagorean fuzzy sets for multiple criteria decision analysis. The proposed method utilizes a novel Pythagorean fuzzy precedence index, which is based on the difference of scalar functions under anchored judgments with respect to the superiority/inferiority Pythagorean fuzzy numbers. To appropriately describe the hesitation between indifference and preference in the Pythagorean fuzzy context, this paper introduces useful precedence-based preference functions to establish the precedence relations based on pairwise comparisons. As a multiple criteria measure under Pythagorean fuzzy uncertainty, the concept of overall preference indices is identified at the aggregation stage to exploit certain rules for generating PROMETHEE flows. Next, this paper provides effective Pythagorean fuzzy PROMETHEE I and II ranking procedures to determine partial and complete preorders, respectively, among competing alternatives. The developed Pythagorean fuzzy PROMETHEE-based outranking approach is comparatively validated using a real-world application concerning the selection problem of bridge construction methods. The solution results along with a comparison analysis demonstrate that the proposed methodology outperforms the comparative approach in terms of reasonability and stability.