A first course in fuzzy logic
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書誌事項
A first course in fuzzy logic
CRC Press, c1997
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注記
Bibliography: p. 245-249
Includes index
内容説明・目次
内容説明
Using material from a successful course on fuzzy logic, this book is an introduction to the theory of fuzzy sets: mathematical objects modeling the vagueness of our natural language when we describe phenomena that do not have sharply defined boundaries. The book provides background information necessary to apply fuzzy set theory in various areas, including engineering, fuzzy logic, and decision making. The exercises at the end of each chapter serve to deepen the reader's understanding of the concepts, and to test their ability to make the necessary calculations.
目次
Chapter 1. The Concept of Fuzziness
Examples
Mathematical Modeling
Some Operations on Fuzzy Sets
Fuzziness as Uncertainty
Exercises
Chapter 2. Some Algebra of Fuzzy Sets
Boolean Algebras and Lattices
Equivalence Relations and Partitions
Composing Mappings
Isomorphisms and Homomorphisms
Alpha-Cuts
Images of Alpha-Level Sets
Exercises
Chapter 3. Fuzzy Quantities
Fuzzy Quantities
Fuzzy Numbers
Fuzzy Intervals
Exercises
Chapter 4. Logical Aspects of Fuzzy Sets
Classical Two-Valued Logic
A Three-Valued Logic
Fuzzy Logic
Fuzzy and Lukasiewicz Logics
Interval-Valued Fuzzy Logic
Probabilistic Logic
Exercises
Chapter 5. Basic Connectives
t-Norms
Generators of t-Norms
Negations
t-Conorms
Fuzzy Implications
Interval-Valued Fuzzy Sets
Sensitivity of Connectives
Exercises
Chapter 6. Fuzzy Relations
Definitions and Examples
Binary Fuzzy Relations
Operations on Fuzzy Relations
Exercises
Chapter 7. Universal Approximation
Fuzzy Rule Bases
Design Methodologies
Some Mathematical Background
Approximation Capability
Exercises
Chapter 8. Possibility Theory
Set Functions
Possibility
Possibility Theory Baesd on Fuzzy Sets
Approximate Reasoning
A Simple Form of Generalized Modus Ponens
The Compositional Rule of Inference
Exercises
Chapter 9. Partial Knowledge
Incomplete Probabilistic Information
Belief Functions
Reasoning with Belief Functions
Decision Making
Exercises
Chapter 10. Fuzzy Measures
Motivation and Definitions
Fuzzy Measures and Lower Probabilities
Fuzzy Measures in Other Areas
Conditional Fuzzy Measures
Exercises
Chapter 11. Fuzzy Integrals
Review of the Lebesgue Integral
The Sugeno Integral
Choquet Integral
The Choquet Integral as a Fuzzy Integral
Exercises
Chapter 12. Fuzzy Modeling
Motivation for Fuzzy Control
The Methodology of Fuzzy Control
Optimal Fuzzy Control
An Analysis of Fuzzy Control Techniques
Approximate Reasoning in Expert Systems
Exercises
Bibliography
Answers to Selected Exercises
Index
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