Corresponding reduction algorithms for relative indiscernibility and discernibility relation were proposed. Firstly, considering the reduction of the relative indiscernibility relation in equivalence relation, the corresponding discernibility matrix was proposed and a reduction algorithm was proposed based on the matrix. Then, a reduction algorithm for relative discernibility relation was proposed according to the complementary relationship of the relation. Secondly, the concepts such as relative indiscernibility relation were expanded to the general relation. The corresponding discernibility matrix was proposed for the relative indiscernibility relation reduction in the relation decision system, and the corresponding discernibility matrix for the relative discernibility relation reduction was obtained by using the complementary relationship of the relation, so the reduction algorithms for both relations were obtained. Finally, the proposed algorithms were verified on the selected UCI datasets. In the equivalence relation, the algorithm of the relative EQuivalence INDiscernibility relation reduction based on absolute reduction (EQIND) and the algorithm of the relative BInary INDiscernibility relation reduction (BⅡND) have the same results. The algorithm of the relative EQuivalence DIScernibility relation reduction based on absolute reduction (EQDIS) and the algorithm of the relative BInary DIScernibility relation reduction (BIDIS) have the same results. Meanwhile, BⅡND and BIDIS are suitable for the incomplete decision table. The feasibility of the proposed algorithms were verified by the experimental results.