Revisiting type-2 triangular norms on normal convex fuzzy truth values.

This paper studies t-norms on the space 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 tr-norm on L, which is strictly stronger than t-norm on L. Furthermore, we characterize some restrictive axioms of tr-norms for convolution operations on L and obtain some necessary conditions for tr-(co)norm convolution operations on L.