A Hybrid Entropy Heronian Outranking Framework for Fuzzy Multi-Criteria Decision Analysis under Uncertainty

Decision-making problems characterized by uncertainty, interdependent criteria, and subjective assessments are common in operations research and multi-criteria decision analysis. This study proposes a hybrid entropy Heronian adaptive framework for fuzzy multi-criteria decision-making, integrating entropy-based objective weighting, Heronian mean aggregation, and adaptive outranking mechanisms. Triangular fuzzy numbers are employed to model linguistic evaluations, while statistical dispersion measures are used to dynamically calibrate preference thresholds. The proposed framework is applied to a representative decision problem to demonstrate its analytical consistency and robustness. Comparative results with established fuzzy outranking and MCDM methods confirm that the proposed approach provides stable rankings, enhanced sensitivity to data variability, and transparent preference modeling. The framework offers a structured and robust decision-support tool suitable for complex decision environments under uncertainty.