Mathematics of Fuzzy Sets and Fuzzy Logic

by Barnabas Bede

Overview

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.

Product Details

ISBN-13:	9783642433023
Publisher:	Springer Berlin Heidelberg
Publication date:	01/28/2015
Series:	Studies in Fuzziness and Soft Computing , #295
Edition description:	2013
Pages:	276
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

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.

Editorial Reviews

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)

From the Publisher