Mathematics of Fuzzy Sets and Fuzzy Logic

Mathematics of Fuzzy Sets and Fuzzy Logic

Hardback Studies in Fuzziness and Soft Computing

By (author) Barnabas Bede

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  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Format: Hardback | 338 pages
  • Dimensions: 160mm x 238mm x 20mm | 558g
  • Publication date: 14 December 2012
  • Publication City/Country: Berlin
  • ISBN 10: 3642352200
  • ISBN 13: 9783642352201
  • Edition: 12000
  • Edition statement: 2013 ed.
  • Illustrations note: 75 black & white illustrations, biography
  • Sales rank: 1,471,212

Product description

This book presents a mathematically-based introduction into the fascinating topic of Fuzzy Sets and Fuzzy Logic and might be used as textbook at both undergraduate and graduate levels and also as reference guide for mathematician, scientists or engineers who would like to get an insight into Fuzzy Logic. Fuzzy Sets have been introduced by Lotfi Zadeh in 1965 and since then, they have been used in many applications. As a consequence, there is a vast literature on the practical applications of fuzzy sets, while theory has a more modest coverage. The main purpose of the present book is to reduce this gap by providing a theoretical introduction into Fuzzy Sets based on Mathematical Analysis and Approximation Theory. Well-known applications, as for example fuzzy control, are also discussed in this book and placed on new ground, a theoretical foundation. Moreover, a few advanced chapters and several new results are included. These comprise, among others, a new systematic and constructive approach for fuzzy inference systems of Mamdani and Takagi-Sugeno types, that investigates their approximation capability by providing new error estimates.

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Review quote

From the reviews: "This is a well-written elementary introduction into the basic mathematical topics for fuzzy sets and fuzzy numbers, accessible for undergraduate mathematics and also for engineering students." (Siegfried J. Gottwald, zbMATH, Vol. 1271, 2013)

Back cover copy

This book presents a mathematically-based introduction into the fascinating topic of Fuzzy Sets and Fuzzy Logic and might be used as textbook at both undergraduate and graduate levels and also as reference guide for mathematician, scientists or engineers who would like to get an insight into Fuzzy Logic. Fuzzy Sets have been introduced by Lotfi Zadeh in 1965 and since then, they have been used in many applications. As a consequence, there is a vast literature on the practical applications of fuzzy sets, while theory has a more modest coverage. The main purpose of the present book is to reduce this gap by providing a theoretical introduction into Fuzzy Sets based on Mathematical Analysis and Approximation Theory. Well-known applications, as for example fuzzy control, are also discussed in this book and placed on new ground, a theoretical foundation. Moreover, a few advanced chapters and several new results are included. These comprise, among others, a new systematic and constructive approach for fuzzy inference systems of Mamdani and Takagi-Sugeno types, that investigates their approximation capability by providing new error estimates. "

Table of contents

1 Fuzzy Sets.- 2 Fuzzy Set-Theoretic Operations.- 3 Fuzzy Relations.- 4 Fuzzy numbers.- 5 Fuzzy Arithmetic.- 6 Fuzzy Inference.- 7 Single Input Single Output Fuzzy Systems.- 8 Fuzzy Analysis.- 9 Fuzzy Differential Equations.- 10 Extensions of Fuzzy Set Theory.- 11 Possibility Theory.- 12 Fuzzy Clustering.- 13 Fuzzy Transform.- 14 Arti cial Neural Networks and Neuro-Fuzzy Systems.