Fuzzy Implications (Hardcover, 2008 ed.)

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."

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Studies in Fuzziness and Soft Computing, 231
Release date:	August 2008
First published:	2008
Authors:	Michal Baczynski • Balasubramaniam Jayaram
Dimensions:	235 x 155 x 19mm (L x W x T)
Format:	Hardcover
Pages:	310
Edition:	2008 ed.
ISBN-13:	978-3-540-69080-1
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematics for scientists & engineers Books > Computing & IT > Applications of computing > Artificial intelligence > General
LSN:	3-540-69080-8
Barcode:	9783540690801

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