# Mathematics of Fuzzy Sets and Fuzzy Logic

• Barnabas Bede
Book

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

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
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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. Barnabas Bede
Pages 247-258
16. Back Matter
Pages 0--1

### Introduction

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.

### Keywords

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

• Barnabas Bede
• 1
1. 1., Department of MathematicsDigiPen Institute Of TechnologyRedmondUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-35221-8
• Copyright Information Springer-Verlag Berlin Heidelberg 2013
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages Engineering
• Print ISBN 978-3-642-35220-1
• Online ISBN 978-3-642-35221-8
• Series Print ISSN 1434-9922
• Series Online ISSN 1860-0808
• Buy this book on publisher's site