This study addresses the challenges of accurate flood forecasting in the context of increasing extreme weather events and climate change. The Lower and Upper Boundary Estimation Method (LUBE) is widely used to quantify uncertainty, but traditional interval prediction evaluation systems rely solely on coverage and width indicators, limiting their effectiveness. To improve this, the authors propose the Prediction Interval Fitting Coefficient (PIFC) and combine it with the Prediction Interval Coverage Probability (PICP) and Normalized Average Width Index (PINAW) to develop the Coverage Width Fitting-Based Criterion (CWFC). This criterion broadens the interval prediction evaluation system. The study also constructs single-objective and multi-objective LUBE interval forecasting models using the Randomized Weighted Particle Swarm Algorithm (RWPSo) and the Non-dominated Sorting Genetic Algorithms III (NSGA-III). Verification results from cascade hydropower stations in the Yalong River Basin show that the introduction of PIFC significantly improves the calculation efficiency and prediction accuracy of the single-target interval prediction model. Under the CWFC objective function, the PINAW and PIFC indexes are significantly better, and the PICP gap is smaller. In multi-objective conditions, the Pareto non-inferior solution set provides more choices for decision-makers. During the flood season, the PICP can reach over 93%, PINAW is controlled below 10%, and PIFC can reach over 0.95, demonstrating significant improvements in interval prediction performance. The research offers a new approach for basin interval prediction.This study addresses the challenges of accurate flood forecasting in the context of increasing extreme weather events and climate change. The Lower and Upper Boundary Estimation Method (LUBE) is widely used to quantify uncertainty, but traditional interval prediction evaluation systems rely solely on coverage and width indicators, limiting their effectiveness. To improve this, the authors propose the Prediction Interval Fitting Coefficient (PIFC) and combine it with the Prediction Interval Coverage Probability (PICP) and Normalized Average Width Index (PINAW) to develop the Coverage Width Fitting-Based Criterion (CWFC). This criterion broadens the interval prediction evaluation system. The study also constructs single-objective and multi-objective LUBE interval forecasting models using the Randomized Weighted Particle Swarm Algorithm (RWPSo) and the Non-dominated Sorting Genetic Algorithms III (NSGA-III). Verification results from cascade hydropower stations in the Yalong River Basin show that the introduction of PIFC significantly improves the calculation efficiency and prediction accuracy of the single-target interval prediction model. Under the CWFC objective function, the PINAW and PIFC indexes are significantly better, and the PICP gap is smaller. In multi-objective conditions, the Pareto non-inferior solution set provides more choices for decision-makers. During the flood season, the PICP can reach over 93%, PINAW is controlled below 10%, and PIFC can reach over 0.95, demonstrating significant improvements in interval prediction performance. The research offers a new approach for basin interval prediction.