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

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.