September 2014
Intermediate to advanced
632 pages
21h 5m
English
Content preview from Soft Computing and Its Applications, Volume One
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308 Soft Computing and Its Applications
(3.65)
where is the Łukasiewicz product is some implication.
Proposition 3.12 Let be the Łukasiewicz implication in (3.65). Then very
for all y.
We have studied the structures of truth value sets in different logical systems.
The list is not exhaustive but sufcient. We nd Heyting, Post, Łukasiewicz, Gaines,
MV-algebras, and continuous T-norms, which dene a residuated lattice. Studies on
implication, category theoretical aspects, some philosophical and other discussions
suggest adjoint couples, and residuated structures. The only cases when we do not nd
this structure seem to be fuzzy logics ...
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