Journal
INFORMATION SCIENCES
Volume 643, Issue -, Pages -Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ins.2023.119246
Keywords
Fuzzy truth values; Triangular norm (t-norm)
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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.
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.
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