Fuzzy cooperative game analysis within the international railway freight coalition framework

International railway freight cooperation is essential for enhancing regional logistics efficiency, especially in the context of rising anti-globalization trends and pandemic-induced disruptions to maritime transport. This study aims to develop a stable and equitable allocation mechanism for freight volume and operating revenue (freight revenue collected by a country's rail system or designated freight operators) under the international rail freight coalition framework. We construct a fuzzy cooperative game model that accounts for export demand, participation levels, transport resource utilization, and return empty load rates. Results from the CSERE case show that the proposed scheme increases total operating revenue by 37.85-204.88% for member countries compared to traditional mileage-based allocations, and reduces the return empty load rate from 40 to 7.83%. The fuzzy coalition model ensures fair compensation for disadvantaged countries and enhances the overall stability of cooperation. These findings offer practical insights for policymakers and rail freight operators aiming to promote efficient multilateral trade logistics. The originality of this work lies in integrating fuzzy coalition game theory with real-world data to address strategic behavior and empty return issues in international rail freight.