Abstract: The decision-theoretic rough sets model is introduced. Problems like the computation of the various decison
domain, the approximation set of the decision rough sets are studied. By introduction of induced matrix of the equivalent rela- tion matrix and the concept of cut matrix, the upper and lower approximation set in decision-theoretic rough set, and then the related decision domain sets are worked out. And the algorithm for determining the related decision domains and the upper and lower approximation sets of decision rough sets are put forth. Lastly, through examples, the concrete operational method for determining the approximation sets is explained and the validity of the algorithm is proved.