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- W4295679985 abstract "It is well known that the usual point-wise ordering over the set T of t-norms makes it a poset but not a lattice, i.e., the point-wise maximum or minimum of two t-norms need not always be a t-norm again. In this work, we propose, two binary operations on the set TCA of continuous Archimedean t-norms and obtain, via these binary operations, a partial order relation ⊑, different from the usual point-wise order ≤, on the set TCA. As an interesting outcome of this structure, some stronger versions of some existing results dealing with the upper and lower bounds of two continuous Archimedean t-norms with respect to the point-wise order ≤ are also obtained. Finally, with the help of the operations on the set TCA, two binary operations ⊕,⊗ on the set TC of continuous t-norms are proposed and showed that (TC,⊕,⊗) is a lattice. Thus we have both a way of generating continuous t-norms from continuous t-norms and also obtain an order on them." @default.
- W4295679985 created "2022-09-14" @default.
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- W4295679985 date "2023-06-01" @default.
- W4295679985 modified "2023-10-18" @default.
- W4295679985 title "Generation of continuous T-norms through latticial operations" @default.
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- W4295679985 doi "https://doi.org/10.1016/j.fss.2022.09.005" @default.
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