Fuzzy Implications by Balasubramaniam Jayaram (English) Paperback Book

Description: Fuzzy Implications by Balasubramaniam Jayaram, Michał Baczyński This book is the first ever to deal exclusively with this class of operations. It offers an introduction to Fuzzy Implications, an analytical study of them, and an algebraic exploration into the structures that exist on the set of all FIs. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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 andYuans book[147],ProfessorLot?A. Zadehstates the following: "The problem is that the term fuzzy logic has two di?erent meanings. Notes First book in the fertile area of fuzzy implication operators Back Cover Fuzzy Implications (FIs) generalize the classical implication and play a similar important role in Fuzzy Logic (FL), both in FL_n and FL_w in the sense of Zadeh. Their importance in applications of FL, viz., Approximate Reasoning (AR), Decision Support Systems, Fuzzy Control (FC), etc., is hard to exaggerate. This treatise is perhaps the first attempt at dealing exclusively with this class of operations. The book begins with an introduction to FIs along with their desirable properties and investigates their inter-relationships. The reminder of the book is divided into 3 parts. Part I is an analytical study of FIs, detailing the different ways of obtaining FIs, generally called as families of FIs, the various properties they satisfy and the overlaps that exist among them. Part II is an algebraic exploration into the structures that exist on the set of all FIs, while the final part highlights the effecting role FIs with their myriad properties play in the inference schemes in AR. This book is intended for any researcher in FL operations and it can serve as an auxiliary textbook for different courses on FL or FC. Parts of this book may also be of interest to practitioners in applications of FL, especially in AR or FC, where FIs play a central role. Table of Contents An Introduction to Fuzzy Implications.- An Introduction to Fuzzy Implications.- I: Analytical Study of Fuzzy Implications.- Fuzzy Implications from Fuzzy Logic Operations.- Fuzzy Implications from Generator Functions.- Intersections between Families of Fuzzy Implications.- Fuzzy Implications from Uninorms.- II: Algebraic Study of Fuzzy Implications.- Algebraic Structures of Fuzzy Implications.- Fuzzy Implications and Some Functional Equations.- III: Applicational Study of Fuzzy Implications.- Fuzzy Implications in Approximate Reasoning. Long Description Nothing new had been done in Logic since Aristotle! -KurtGodel Feature First book in the fertile area of fuzzy implication operators Details ISBN3642088619 Author Micha Baczyski Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Series Studies in Fuzziness and Soft Computing Year 2010 ISBN-10 3642088619 ISBN-13 9783642088612 Format Paperback Publication Date 2010-10-21 Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany DEWEY 620 Edition 1st Short Title FUZZY IMPLICATIONS Language English Media Book Series Number 231 Pages 310 Edition Description Softcover reprint of hardcover 1st ed. 2008 Alternative 9783540690801 Illustrations XVIII, 310 p. Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96237281;

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