In ordered decision information systems, an interval is defined as a set of objects which are dominated by a specific object and meanwhile dominate another specific object. The intervals are taken as basic knowledge granules, and used to develop a new dominance-based rough set approach. With this model, the interval decision rule whose decision values fall into a specific interval can be induced. The reduct of an interval is defined, and the discernibility function is constructed to compute the reducts of the interval. By reducts of an interval, corresponding optimal interval decision rules can be obtained. The proposed approach is more flexible than the original dominance-based rough set approach, and the induced decision rules can be directly used in classification of ordinal data.