We study the problem of classifying interval-based temporal sequences (IBTSs). Since common classification algorithms cannot be directly applied to IBTSs, the main challenge is to define a set of features that effectively represents the data such that classifiers can be applied. Most prior work utilizes frequent pattern mining to define a feature set based on discovered patterns. However, frequent pattern mining is computationally expensive and often discovers many irrelevant patterns. To address this shortcoming, we propose the FIBS framework for classifying IBTSs. FIBS extracts features relevant to classification from IBTSs based on relative frequency and temporal relations. To avoid selecting irrelevant features, a filter-based selection strategy is incorporated into FIBS. Our empirical evaluation on eight real-world datasets demonstrates the effectiveness of our methods in practice. The results provide evidence that FIBS effectively represents IBTSs for classification algorithms, which contributes to similar or significantly better accuracy compared to state-of-the-art competitors. It also suggests that the feature selection strategy is beneficial to FIBS's performance.