Abstract: The triangular norms and their adjoint properties on the interval-valued set are discussed, and some important results are obtained.By using the triangular norms and implication operators on the interval-valued set, the formulas of solutions of CRI algorithms for interval-valued fuzzy reasoning of FMP and FMT problems are worked out respectively.Aiming at the triangular modules and implication operators on interval-valued set, particularly the residual adjoint pair, the reductive properties of CRI algorithm for interval-valued fuzzy reasoning of FMP and FMT are discussed.