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Fuzzy Implications (Paperback, Softcover reprint of hardcover 1st ed. 2008)
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Fuzzy Implications (Paperback, Softcover reprint of hardcover 1st ed. 2008)
Series: Studies in Fuzziness and Soft Computing, 231
Expected to ship within 10 - 15 working days
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Nothing new had been done in Logic since Aristotle -KurtGodel ]
(1906-1978) Fuzzyimplicationsareoneof themain operationsinfuzzy
logic.Theygeneralize the classical implication, which takes values
in {0,1}, to fuzzy logic, where the truth values belong to the unit
interval 0,1]. In classical logic the implication
canbede?nedindi?erentways.Threeofthesehavecometo assumegreatert-
oreticalimportance, viz. the usual materialimplication from the
Kleene algebra, the implication obtained as the residuum of the
conjunction in Heyting algebra (also called pseudo-Boolean algebra)
in the intuitionistic logic framework and the implication (also
called as 'Sasaki arrow') in the setting of quantum logic.
Interestingly, despite their di?ering de?nitions, their truth
tables are identical in classical case. However, the natural
generalizations of the above de?nitions in the fuzzy logic
framework are not identical. This diversity is more a boon than a
bane and has led to some intensive research on fuzzy implications
for close to three decades. It will be our endeavor to cover the
various works churned out in this period to su?cient depth and
allowable breadth in this treatise. In the forewordto Klir
andYuan's book 147], ProfessorLot?A. Zadehstates the following:
"The problem is that the term 'fuzzy logic' has two di?erent
meanings."
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