Sinossi
This text introduces the reader to basic concepts and techniques in the field of fuzzy sets and gives an account of the literature. It does not treat applications, but rather provides a theoretical foundation for applying fuzzy set theory. The main topics which are treated are: basic set theory, basic lattice theory, operations on fuzzy sets, t-norms and t-conorms, special types of fuzzy sets, fuzzy relations, functions working on fuzzy sets, fuzzy real numbers (both probabilistic and non-probabilistic), basic classical logic and fundamentals concerning fuzzy logic. This volume is intended for researchers working in the areas of engineering, data analysis, control theory, pattern recognition, neural networks, clustering, expert systems, information retrieval, operations research, decision-making, image and signal processing, and for those who require more information on the set-theoretical basics on which fuzzy set theory is founded.
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Contenuti
List of Figures. Preface. 1: Elementary Set Theory. 1. Sets and subsets. 2. Functions and relations. 3. Partially ordered sets. 4. The lattice of subsets of a set. 5. Characteristic functions. 6. Notes. 2: Fuzzy Sets. 1. Definitions and examples. 2. Lattice theoretical operations on fuzzy sets. 3. Pseudocomplementation. 4. Fuzzy sets, functions and fuzzy relations. 5. alpha-levels. 6. Notes. 3: t-Norms, t-Conorms and Negations. 1. Pointwise extensions. 2. t-Norms and t-Conorms. 3. Negations. 4. Notes. 4: Special Types of Fuzzy Sets. 1. Normal fuzzy sets. 2. Convex fuzzy sets. 3. Piecewise linear fuzzy sets. 4. Compact fuzzy sets. 5. Notes. 5: Fuzzy Real Numbers. 1. The probabilistic view. 2. The non-probabilistic view. 3. Interpolation. 4. Notes. 6: Fuzzy Logic. 1. Connectives in classical logic. 2. Fundamental classical theorems. 3. Basic principles of fuzzy logic. 4. Lattice generated fuzzy connectives. 5. t-Norm generated fuzzy connectives. 6. Probabilistically generated fuzzy connectives. 7. Notes. 7: Bibliography. 1. Books. 2. Articles. Index.
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Fuzzy Set Theory: Basic Concepts, Techniques and Bibliography
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Fuzzy Set Theory
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Springer Netherlands Mai 1996, 1996
ISBN 10: 0792340574
ISBN 13: 9780792340577
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 428 pp. Englisch. Codice articolo 9780792340577
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Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 pla. Codice articolo 5967777
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Condizione: New. Introduces the reader to basic concepts and techniques in the field of fuzzy sets and gives an account of the literature. This book covers topics including: basic set theory, basic lattice theory, operations on fuzzy sets, t-norms and t-conorms, special types of fuzzy sets, fuzzy relations, functions working on fuzzy sets, and fuzzy real numbers. Num Pages: 408 pages, biography. BIC Classification: PBCH; PBWX. Category: (P) Professional & Vocational. Dimension: 234 x 156 x 23. Weight in Grams: 774. . 1996. Hardback. . . . . Codice articolo V9780792340577
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