Explainable Multi-Criteria Decision Analysis for Supply Chain Risk Management: An Integrated FRAM-AHP-XAI Framework with Theoretical Foundations

Supply chain decision-making under uncertainty requires integrating quantitative risk assessment with interpretable artificial intelligence. This paper extends the FRAM-AHP (Functional Resonance Analysis Method - Analytical Hierarchy Process) framework by embedding explainable AI (XAI) techniques to enhance transparency in multi-criteria risk prioritization. We introduce a theoretical foundation through a novel theorem establishing how functional variability propagates through decision hierarchies, along with a formal proposition on AI-augmented optimization strategies. Our framework combines MCDA principles with machine learning interpretability (LIME and SHAP) to ensure decision transparency for supply chain managers. We demonstrate that integrating functional resonance theory with explainable decision models reduces decision bias by quantifying the impact of operational variability on risk priorities. Computational experiments on real supply chain datasets show that the framework achieves 27% improvement in decision consistency while maintaining full interpretability