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

Automated summary

This paper studies the t-norms on the space L of all normal and convex fuzzy truth values. It proves that the non-convolution form type-2 t-norm constructed by Wu et al. is the only one that satisfies the distributivity law for meet-convolution. It also shows that the t-norm in the sense of Walker and Walker is strictly stronger than the t-norm on L.