In this paper we consider a special class of t-norms TT1,T2,t on the lattice LI , where LI is the underlying lattice of both intuitionistic fuzzy set theory (Atanassov, 1983) and interval-valued fuzzy set theory (Sambuc, 1975). We investigate under which conditions these tnorms are meet-morphisms. Using these results, we obtain a characterization for t-norms on LI which are both joinand meet-mo...