A novel dynamic fare pricing model based on fuzzy bi-level programming for subway systems with heterogeneous passengers

•Proposing a dynamic fare pricing model utilizing demand prediction congestion.•We propose Kumaraswamy membership function to construct fuzzy sets in our study.•A TSK fuzzy logic system has been applied for passenger demand prediction.•A fuzzy bi-level programming model has been developed for fare price determination.•Effect of CODID-19 situation has been considered in our experiments.