A New Ranking Framework for Multi-Criteria Decision Making with Fuzzy Numbers Using Referential Alpha Cut Analysis

In today’s world, intelligent systems for decision-making are continuously evolving, highlighting the importance of accurately ranking and prioritizing available alternatives. Fuzzy sets and fuzzy numbers are widely used to model complex problems, making the ranking of fuzzy numbers essential in decision-making. However, several existing score functions face difficulties in distinguishing highly overlapping fuzzy numbers and fuzzy numbers with identical cores but different support values. In some cases, these methods may also assign identical scores to distinct fuzzy numbers, resulting in ambiguous and inconsistent rankings. To address these issues, this paper proposes a novel score function based on referential fuzzy numbers to improve ranking accuracy and provide more reliable results. The proposed score function is developed from a referential fuzzy number by combining the arithmetic mean of the alpha-cut midpoints and widths to construct an uncertainty ratio, thereby incorporating both the representative value and the uncertainty of generalized trapezoidal fuzzy numbers into the ranking process. To show its effectiveness, several fuzzy numbers are evaluated and compared with existing methods. Furthermore, a Multi-Criteria Decision-Making application is solved using two modified techniques, namely modified fuzzy TOPSIS and modified WASPAS. Finally, a sensitivity analysis is conducted to evaluate the stability of the proposed method.