Post-earthquake emergency resource allocation requires rapid, scientific decision-making under information incompleteness and uncertainty, where traditional deterministic approaches are inadequate. This study proposes a group decision-making framework for post-earthquake rescue priority evaluation, which combines interval-valued preference representation and optimization-based incomplete matrix completion. It extends the interval Analytic Hierarchy Process (IAHP) to non-complete information environments with a multi-objective optimization model (MOP4) to recover missing entries while maintaining consistency. Sufficient conditions for full matrix consistency are established, and a possibility degree-based ranking mechanism is used to get priority orderings. The framework is validated in a real post-earthquake rescue prioritization case in central Myanmar (including Sagaing Division) following the March 28, 2025, 7.9-magnitude seismic event. Four criteria are assessed by experts under partial information. Results show X7 and X5 are top-priority for immediate rescue, and reveal a tension between rescue urgency and feasibility that single-criterion approaches miss. Comparative analysis confirms the framework's robustness, consistency, and adaptability compared to conventional approaches. The findings contribute to uncertain group decision-making theory and provide tools for emergency management within the 72 - hour post-disaster window.