Since anomalies are usually caused by changes in shape and amplitude in time series data, and most of the interval‐based methods utilized appear in the literature from a global perspective to detect anomalies. Nevertheless, the anomalies are also usually caused by local changes in shape and amplitude. Following these limitations, an enhanced interval‐based approach based on the interval information granules with the principle of justifiable granularity, viz., the EIA method, is formulated in this study for anomaly detection. First, the interval information granules are produced separately from the global and local perspectives in an abstracted manner on the basis of this principle. An interval‐based similarity measurement algorithm is then designed based on the abstraction results to calculate the anomaly scores from the various interval information granules for anomaly detection. Compared with classical methods, the proposed approach exhibits better performance in terms of data anomaly resolution and detection accuracy, which have been verified and supported in much of real‐world data. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.