Fuzzy Set Theory

1. Front Matter

   Pages i-xiv

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2. Elementary Set Theory

   • R. Lowen

   Pages 1-19

3. Fuzzy Sets

   • R. Lowen

   Pages 21-47

4. t-Norms, t-Conorms and Negations

   • R. Lowen

   Pages 49-132

5. Special Types of Fuzzy Sets

   • R. Lowen

   Pages 133-141

6. Fuzzy Real Numbers

   • R. Lowen

   Pages 143-168

7. Fuzzy Logic

   • R. Lowen

   Pages 169-239

8. Bibliography

   • R. Lowen

   Pages 241-404

9. Back Matter

   Pages 405-408

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The purpose of this book is to provide the reader who is interested in applications of fuzzy set theory, in the first place with a text to which he or she can refer for the basic theoretical ideas, concepts and techniques in this field and in the second place with a vast and up to date account of the literature. Although there are now many books about fuzzy set theory, and mainly about its applications, e. g. in control theory, there is not really a book available which introduces the elementary theory of fuzzy sets, in what I would like to call "a good degree of generality". To write a book which would treat the entire range of results concerning the basic theoretical concepts in great detail and which would also deal with all possible variants and alternatives of the theory, such as e. g. rough sets and L-fuzzy sets for arbitrary lattices L, with the possibility-probability theories and interpretations, with the foundation of fuzzy set theory via multi-valued logic or via categorical methods and so on, would have been an altogether different project. This book is far more modest in its mathematical content and in its scope.

• Extension
• Pattern Recognition
• cognition
• control
• expert system
• fuzzy
• fuzzy logic
• fuzzy sets
• linear optimization
• neural networks
• operations research
• set theory
• sets

• Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium

  R. Lowen

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