Rough sets theory has proved to be a useful mathematical tool for classification and prediction. However, as many real-world problems deal with ordering objects instead of classifying objects, one of the extensions of the classical rough sets approach is the dominance-based rough sets approach, which is mainly based on substitution of the indiscernibility relation by a dominance relation. In this article, we present a dominance-based rough sets approach to reasoning in incomplete ordered information systems. The approach shows how to find decision rules directly from an incomplete ordered decision table. We propose a reduction of knowledge that eliminates only that information that is not essential from the point of view of the ordering of objects or decision rules. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 13–27, 2005.