Abstract: A partial ordering relation is presented in the incomplete interval-valued information system(IIIS) with the purpose of classification,and practical approaches are given to reduce the partial ordering relation.Then a rough set model based on the partial ordering relationship can be constructed and the concepts of lower and upper approximate reduction are introduced into the incomplete interval-valued decision system(IIDS).These two types of reduction are minimal subsets of the attributes,which can preserve the lower and upper approximations of all decision classes respectively.With these reductions,the simplified decision rules can be obtained.