  This paper studies t-norms on the space $\mathbf{L}$ of all normal and convex
fuzzy truth values. We first prove that the only non-convolution form type-2
t-norm constructed by Wu et al. satisfies the distributivity law for
meet-convolution and show that t-norm in the sense of Walker and Walker is
strictly stronger than t$_{r}$-norm on $\mathbf{L}$, which is strictly stronger
than t-norm on $\mathbf{L}$. Furthermore, we characterize some restrictive
axioms of t$_{r}$-norms for convolution operations on $\mathbf{L}$ and obtain
some necessary conditions for t$_{r}$-(co)norm convolution operations on
$\mathbf{L}$ .
