Prediction methods have become a hot topic in intelligent decision making. Most of the existing prediction methods focus on the prediction accuracy and stability. As a second choice, accurate interval prediction can provide a relatively reliable reference in the sense of probability and provide help for assisting decision management. Therefore, we propose a novel interval prediction approach. Firstly, the decomposition method based on ensemble empirical mode decomposition (EEMD) is utilized to alleviate the complexity of the original time series, thereby generating a series of relatively smooth subseries. Secondly, a three-way clustering (TWC) algorithm is established by integrating sample entropy into probabilistic rough set, enriching the three-way clustering theory from the perspective of entropy. Thirdly, aiming at determining the optimal input dimensions of different neural networks, the feature selection technique based on phase space reconstruction (PSR) is constructed. Furthermore, an interval prediction system based on TWC is proposed to provide a new data-driven prediction method. Finally, the proposed approach is applied to predict the interval price of crude oil. On the one hand, the practicability of the constructed prediction approach is verified; on the other hand, it provides a new theoretical method for interval prediction of crude oil price. The experiment results show the proposed prediction approach can assist the decision-makers to make scientific and reasonable decisions. (C) 2022 Published by Elsevier B.V.