© 2013

Mathematics of Fuzzy Sets and Fuzzy Logic


  • Comprehensive introduction into Fuzzy Set Theory, Fuzzy Logic, and some areas of Computational Intelligence that are strongly related to Fuzzy Sets

  • The book is intended to cover most of the basic topics in Fuzzy Sets Theory and Fuzzy Logic from a mathematical point of view as well as most of the current applications of the presented theory and can be used as textbook at both undergraduate and graduate levels

  • Written by a leading expert in the field


Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 295)

Table of contents

  1. Front Matter
    Pages 1-10
  2. Barnabas Bede
    Pages 1-12
  3. Barnabas Bede
    Pages 13-31
  4. Barnabas Bede
    Pages 33-49
  5. Barnabas Bede
    Pages 51-64
  6. Barnabas Bede
    Pages 65-78
  7. Barnabas Bede
    Pages 79-103
  8. Barnabas Bede
    Pages 105-136
  9. Barnabas Bede
    Pages 137-170
  10. Barnabas Bede
    Pages 171-191
  11. Barnabas Bede
    Pages 193-199
  12. Barnabas Bede
    Pages 201-212
  13. Barnabas Bede
    Pages 213-219
  14. Barnabas Bede
    Pages 221-246
  15. Back Matter
    Pages 0--1

About this book


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.



Artificial Neural Network Fuzzy Control Fuzzy Differential Equation Fuzzy Inference System Fuzzy Logic Fuzzy Measure Fuzzy Number Fuzzy Set Genetic Fuzzy System Neuro-Fuzzy System

Authors and affiliations

  1. 1., Department of MathematicsDigiPen Institute Of TechnologyRedmondUSA

Bibliographic information

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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)