This paper introduces a new method for flood interval forecasting, considering interval fitting coefficients. The study proposes the prediction interval fitting coefficient (PIFC) to enhance the evaluation system of interval prediction. By combining PIFC with prediction interval coverage probability (PICP) and normalized average width index (PINAW), a new criterion called coverage width fitting-based criterion (CWFC) is developed. This improves the evaluation dimension of interval prediction. The study constructs single-objective and multi-objective LUBE interval forecasting models based on randomized weighted particle swarm algorithm (RWPSO) and non-dominated sorting genetic algorithms III (NSGA-III). Verification results from cascade hydropower stations in the Yalong river basin show that the single-objective interval prediction model's calculation efficiency and prediction effect are improved after introducing PIFC. Under the CWFC objective function, the PINAW and PIFC indexes in the prediction interval are significantly better, and the PICP gap is smaller. Under multi-objective conditions, the Pareto non-inferior solution set provides more choices for decision makers. During the flood season, PICP can reach more than 93%, PINAW is controlled below 10%, and PIFC can reach more than 0.95. This proves that the performance of interval prediction has been significantly improved after introducing PIFC. The research results provide a new way for basin interval prediction. Flood is a common natural disaster that affects millions of people and causes huge economic damage. Accurate and reliable flood forecasting is essential for ensuring human safety and stable development. Traditional deterministic flood forecasting methods face challenges due to complex hydrological characteristics and model parameter uncertainties. Interval forecasting methods, such as Delta, Bayesian, Bootstrap, LUBE, and GLUE, are used to reflect uncertainty in runoff. However, these methods have limitations, such as requiring specific error distributions or subjective assumptions. The new method improves interval forecasting by introducing PIFC, enhancing the accuracy and reliability of flood prediction. This research provides a new approach for basin interval prediction.This paper introduces a new method for flood interval forecasting, considering interval fitting coefficients. The study proposes the prediction interval fitting coefficient (PIFC) to enhance the evaluation system of interval prediction. By combining PIFC with prediction interval coverage probability (PICP) and normalized average width index (PINAW), a new criterion called coverage width fitting-based criterion (CWFC) is developed. This improves the evaluation dimension of interval prediction. The study constructs single-objective and multi-objective LUBE interval forecasting models based on randomized weighted particle swarm algorithm (RWPSO) and non-dominated sorting genetic algorithms III (NSGA-III). Verification results from cascade hydropower stations in the Yalong river basin show that the single-objective interval prediction model's calculation efficiency and prediction effect are improved after introducing PIFC. Under the CWFC objective function, the PINAW and PIFC indexes in the prediction interval are significantly better, and the PICP gap is smaller. Under multi-objective conditions, the Pareto non-inferior solution set provides more choices for decision makers. During the flood season, PICP can reach more than 93%, PINAW is controlled below 10%, and PIFC can reach more than 0.95. This proves that the performance of interval prediction has been significantly improved after introducing PIFC. The research results provide a new way for basin interval prediction. Flood is a common natural disaster that affects millions of people and causes huge economic damage. Accurate and reliable flood forecasting is essential for ensuring human safety and stable development. Traditional deterministic flood forecasting methods face challenges due to complex hydrological characteristics and model parameter uncertainties. Interval forecasting methods, such as Delta, Bayesian, Bootstrap, LUBE, and GLUE, are used to reflect uncertainty in runoff. However, these methods have limitations, such as requiring specific error distributions or subjective assumptions. The new method improves interval forecasting by introducing PIFC, enhancing the accuracy and reliability of flood prediction. This research provides a new approach for basin interval prediction.