A Four-Reference-Point Sliding-Window Game-Theoretic Model for Sustainable Emergency Decision-Making

To address high uncertainty, dynamic evolution, and limited information in emergency decision-making for major sudden disasters, this paper proposes a sliding-window game-theoretic method with four reference points for emergency response selection. Firstly, interval-valued T-spherical fuzzy sets are adopted to capture decision-makers’ uncertain and hesitant evaluations in interval form. Subsequently, a four-reference-point framework, including the external, internal, average development speed, and ideal proximity reference points, is established to reflect stage-dependent psychological baselines. Furthermore, criterion weights are updated by a sliding-window game-theoretic combination weighting scheme that integrates entropy, anti-entropy, criteria importance through intercriteria correlation, and the coefficient of variation, and performs rolling updates across stages. Prospect values are then computed relative to the four reference points and aggregated to rank alternatives at each stage. Finally, a case study of the 2024 Huludao extreme rainfall event applies the proposed method to evaluate four candidate schemes across six criteria over three decision stages. Results show that rescue cost has the highest weight in all stages, while the importance of rescue speed decreases and social impact increases as the response progresses. The proposed method identifies a comprehensive flood relief scheme led by the People’s Liberation Army and the People’s Armed Police Force as the best option in all stages, because it achieves the highest comprehensive prospect values among all alternatives. Comparative analyses indicate more consistent identification of the optimal scheme than existing approaches, supporting sustainable and resource-efficient disaster management.