A phase-equilibrium outranking method with hysteresis-banded thresholds for robust multi-criteria decision making: PEOM.

Real-world decisions often combine non-compensatory "must-meet" constraints with compensatory trade-offs. Classical Multi-Criteria Decision Making (MCDM) methods (e.g., TOPSIS, VIKOR, PROMETHEE) are mainly compensatory and may rank alternatives highly even when a critical requirement fails. This paper proposes the Phase-Equilibrium Outranking Method (PEOM), a novel hybrid framework that treats hard and soft thresholds as critical frontiers. PEOM integrates: (i) hysteresis-banded thresholds to model strict elimination and gradual penalty zones; (ii) an AND/OR process-aware structure that separates non-compensatory from compensatory criteria; (iii) shrinkage-based weight adjustment to mitigate distortions from correlated indicators; and (iv) a net-flow outranking mechanism for stable, interpretable rankings. PEOM is demonstrated on two energy case studies: wind turbine siting (capacity factor as a veto criterion) and PEM fuel cell hydrogen supply (ISO/SAE purity compliance as a gate). Results show early removal of infeasible options, robustness under correlated criteria, and rankings consistent with engineering intuition, with applicability across domains requiring both constraints and trade-offs.