The decision system can be divided into coordinated decision system and uncoordinated decision system. Generally, the reductions of these two kinds of systems are inconsistent. This paper first introduces the basic concepts of relative reduction, relative belief reduction and relative plausibility reduction, and then sufficient unnecessary conditions of intuitionistic fuzzy rough sets with numerical characteristics are given. It is proven that the upper and lower approximation operators are additive and multiplicative. Then, the consistency of the decision system is analyzed. It turns out that...