首页|The relationships between type-2 t-norms on normal convex fuzzy truth values
The relationships between type-2 t-norms on normal convex fuzzy truth values
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NETL
NSTL
Elsevier
Recent literature has mainly focused on four forms of type-2 t-norms on F-NC composed of all normal convex fuzzy truth values: t-norms defined on the complete lattice, t(ln)-norms defined by Hernandez et al., t(r)-norms defined by Harding et al., and t(lo)-norms defined by Wu et al. The paper studies the relationships among these four types of type-2 t-norms constructed by generalized extended t-norms that come from the generalization of Zadeh's extension principle. Firstly, we sequentially characterize the conditions under which generalized extended t-norms satisfy each restrictive axiom in the definitions of type-2 t-norms, particularly closure properties. Then, we prove that on F-NC, generalized extended t-norms being t(r)-norms (resp. t(lor)-norms) is equivalent to them being t(lo)-norms (resp. t(lor)-norms). Finally, through examples, we demonstrate that on F-NC, t(lo)-norms (resp. t(lor)-norms) are strictly stronger than t-norms (resp. t(r)-norms) even if all of them are constructed by generalized extended t-norms.
Type-2 t-normsGeneralized extended t-normsNormal convex fuzzy truth values
Zhang, Wei、Hu, Bao Qing、Wu, Xinxing
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Southwestern Univ Finance & Econ
Guangxi Minzu Univ||Wuhan University School of Mathematics and Statistics
NETL
NSTL
Elsevier
