Abstract
This paper introduces trapezoidal-valued Fermatean fuzzy (TpVFF) numbers based on the Aczel-Alsina (AA) t-norm and t-conorm operations. New operational laws, including addition, multiplication, and scalar multiplication, are defined. Based on these operations, several geometric aggregation operators, including weighted, ordered weighted, and hybrid operators, are developed, and their fundamental properties are established. A TOPSIS-based multi-criteria group decision-making method is proposed within the developed framework. An illustrative disaster relief allocation problem using the TpVFF-TOPSIS framework demonstrates the applicability of the proposed approach. Sensitivity and Monte Carlo analyses are conducted to examine variations in the decision results under changes in the AA parameter and criterion weights. The results indicate that the ranking is sensitive to changes in the AA parameter and criterion weights, although it remains unchanged in a substantial proportion of the tested scenarios.