The membership of interval-valued fuzzy sets leads to more degree of freedom, which brings superiority in proceeding uncertainty and fuzzification of informations more than classic fuzzy sets.For beter application of interval-valued fuzzy sets, it’s of importance to study it’s cuts and properties.In this paper, we define a kind of t-norm based cuts of interval-valued fuzzy sets, and then discuss the properties of cuts of generalized intersection, union and complement based on t-norm interval-valued fuzzy sets.Specialy, iT(S)i∧(∨)representable, then the intersection, union and complement are commutative with cut set.