Fuzzy Sets and Systems

Name: Fuzzy Sets and Systems | Theory and Applications
Brand: Academic Press
Price: 54.95 EUR
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Theory and Applications

Didier J. DuBois(Autor*in)

Academic Press

Erschienen am 1. Dezember 1980

393 Seiten

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978-0-08-091772-6 (ISBN)

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Front Cover
Fuzzy Sets and Systems: Theory and Applications
Copyright Page
Contents
Foreword
Preface
Acknowledgments
Part I: Introduction
Introduction
Appendix: Some Historical and Bibliographical Remarks
References
Part II: Mathematical Tools
Chapter 1. Fuzzy Sets
A. Definitions
B. Set-Theoretic Operations
C. a-Cuts
D. Cardinality of a Fuzzy Set
E. Inclusions and Equalities of Fuzzy Sets
F. Convex Fuzzy Sets and Fuzzy Structured Sets
G. L-Fuzzy Sets
H. Measures of Fuzziness
References
Chapter 2. Extension Principle, Extended Operations, and Extended Fuzzy Sets
A. Extension Principle
B. Extended Real Operations
C. Extended Fuzzy Sets
References
Chapter 3. Fuzzy Relations
A. n-Ary Fuzzy Relations
B. Binary Fuzzy Relations
C. Similarity Relations and Related Topics
D. Fuzzy Orderings
E. Equations of Fuzzy Relations
F. Generalized Fuzzy Relations
References
Chapter 4. Fuzzy Functions
A. Various Kinds of Fuzzy Functions
B. Fuzzy Extremum
C. Integration of Fuzzy Functions over (Non)Fuzzy Intervals
D. Differentiation
E. Fuzzy Topology
F. Categories of Fuzzy Sets
References
Chapter 5. Fuzzy Measures, Probabilities/Possibilities
A. Fuzzy Measures and Sugeno's Integrals
B. Possibility and Probability
C. Fuzzy Events
D. Fuzzy Distributions
References
Part III: Fuzzy Models and Formal Structures
Chapter 1. Multivalent and Fuzzy Logics
A. Fuzzy Switching Logic
B. Multivalent Logics
C. Fuzzy Modal Logic
D. Fuzzy-Valued Logics
E. Approximate Reasoning
References
Chapter 2. Dynamic Fuzzy Systems
A. Complexity and Fuzziness in System Theory
B. Discrete-Time Fuzzy Systems
C. Fuzzy Automata
D. Deterministic Systems in a Fuzzy Environment
E. Linear Fuzzy Systems
F. Other Topics Related to Fuzziness and Systems
References
Chapter 3. Fuzzy Languages-Fuzzy Algorithms
A. Fuzzy Languages and Fuzzy Grammars
B. Fuzzy Algorithms
References
Chapter 4. Fuzzy Models tor Operations Research
A. Optimization in a Fuzzy Environment
B. Fuzzy Graphs
References
Part IV: Systems-Oriented Fuzzy Topics
Chapter 1. Where Do "They" Come From?
A. Informal Preliminary Discussion
B. Practical Estimation of Membership Functions
C. Identification of Fuzzy Set Operators
D. Tolerance Analysis Using Fuzzy Sets
References
Chapter 2. From Programming Languages to Natural Languages
A. Fuzzy Programming Languages
B. Modeling Natural Languages
C. Deductive Verbal Dynamic Systems
References
Chapter 3. Fuzzy Sets in Decision-Making
A. Fuzzy Rank-Ordering
B. Multicriteria Decision-Making
C. Aggregation of Opinions in a Social Group. Consensus
D. Decision-Making under Randomness and Fuzziness
References
Chapter 4. Fuzzy Control
A. Fuzzy Optimal Control
B. Synthesis of Linguistic Controllers
References
Chapter 5. Fuzzy Sets in Learning Systems
A. Learning with Automata or Fuzzy Conditional Measures
B. Self-Improvement of Fuzzy Linguistic Controllers
References
Chapter 6. Pattern Classification with Fuzzy Sets
A. Pattern Recognition
B. Clustering Algorithms
C. Information Retrieval
References
Chapter 7. Fuzzy Diagnosis
A. Discrimination of Fuzzy States in a Probabilistic Environment
B. Representation of Causality by Fuzzy Relations
References
Chapter 8. Fuzzy Sets in the Identification of Structures
A. Fuzzy Structural Modeling
B. Heuristic Structure Synthesis
C. Fuzzy Grammar Inference
References
Chapter 9. Fuzzy Games
References
Chapter 10. Fuzzy Sets and Catastrophes
References
Part V: A Survey of Potential Applications
A. Artificial Intelligence and Robotics
B. Image Processing and Speech Recognition
C. Biological and Medical Sciences
D. Control
E. Applied Operations Research
F. Economics and Geography
G. Sociology
H. Psychology
I. Linguistics
J. Semiotics
K. Other Topics
References
Conclusion
References in the Nonfuzzy Literature
List of the Most Commonly Used Symbols
Author Index
Subject Index

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