Overview
- First book in the fertile area of fuzzy implication operators
- Includes supplementary material: sn.pub/extras
Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ)
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About this book
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.
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Table of contents (8 chapters)
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Front Matter
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An Introduction to Fuzzy Implications
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Part I: Analytical Study of Fuzzy Implications
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Front Matter
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Part II: Algebraic Study of Fuzzy Implications
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Front Matter
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Part III: Applicational Study of Fuzzy Implications
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Front Matter
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Back Matter
Bibliographic Information
Book Title: Fuzzy Implications
Authors: Michał Baczyński, Balasubramaniam Jayaram
Series Title: Studies in Fuzziness and Soft Computing
DOI: https://doi.org/10.1007/978-3-540-69082-5
Publisher: Springer Berlin, Heidelberg
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2008
Hardcover ISBN: 978-3-540-69080-1Published: 25 August 2008
Softcover ISBN: 978-3-642-08861-2Published: 21 October 2010
eBook ISBN: 978-3-540-69082-5Published: 18 September 2008
Series ISSN: 1434-9922
Series E-ISSN: 1860-0808
Edition Number: 1
Number of Pages: XVIII, 310
Topics: Mathematical and Computational Engineering, Artificial Intelligence, Applications of Mathematics, Operator Theory, Algebra