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Mathematics of Fuzzy Sets and Fuzzy Logic

Barnabas Bede
Publication Date: 
Number of Pages: 
Studies in Fuziness and Soft Computing 295
[Reviewed by
Don Vestal
, on

One of the cornerstones of modern mathematics is the notion that everything can be built on the foundation of set theory. With that in mind, Bede starts with the notion of a fuzzy set: a function \(A:X \longrightarrow [0,1]\), where the value \(A(x)\) denotes the membership degree of \(x\) in the fuzzy set \(A\). From this, the author develops the theory of fuzzy sets and fuzzy logic. This includes fuzzy sets, fuzzy relations, fuzzy numbers, Single Input Single Output fuzzy systems, fuzzy analysis and topology, fuzzy differential equations, and fuzzy transforms.

The material is presented from a mostly theoretical point of view, and each chapter ends with a section of exercises. So the book can be used as a textbook in graduate and (maybe) undergraduate courses in mathematics or computer science, provided the students have a decent mathematics background. Appendices for the mathematical prerequisites are included, covering lattices, real numbers, metric spaces, continuity and normed spaces.

Donald L. Vestal is an Associate Professor of Mathematics at South Dakota State University. His interests include number theory, combinatorics, spending time with his family, and working on his hot sauce collection. He can be reached at Donald.Vestal(AT)

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 Artificial Neural Networks and Neuro-Fuzzy Systems.