A first course in fuzzy logic
著者
書誌事項
A first course in fuzzy logic
Chapman & Hall/CRC, c2000
2nd ed
大学図書館所蔵 全28件
注記
Includes bibliographical references (p. 335-349) and index
内容説明・目次
内容説明
The second edition of the popular A First Course in Fuzzy Logic will continue to provide the ideal introduction to the theory and applications of fuzzy logic. The authors provide a firm mathematical basis for the calculus of fuzzy concepts-necessary to design intelligent systems-and give the student a solid background for further studies and real-world applications.
This new edition provides many new exercises designed to enhance the reader's understanding of the concepts. The authors have expanded on the algebra background needed for the more advanced topics, and include significant new material on basic connectives and the algebraic properties of fuzzy logic, rough sets, conditional events, distributions of random sets, and derivatives of fuzzy measures.
With its comprehensive updates, A First Course in Fuzzy Logic, Second Edition presents all the background necessary for students to begin using fuzzy logic in its many-and rapidly growing-applications.
目次
THE CONCEPT OF FUZZINESS
Examples
Mathematical Modeling
Some Operations on Fuzzy Sets
Fuzziness as Uncertainity
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
FUZZY QUANTITIES
Fuzzy Quantities
Fuzzy Numbers
Fuzzy Intervals
LOGICAL ASPECTS OF FUZZY SETS
Classical Two-Valued Logic
A Three-Valued Logic
Fuzzy Logic
Fuzzy and Lukasiewicz Logics
Interval Valued Fuzzy Logic
Canonical Forms
Notes on Probabilistic Logic
BASIC CONNECTIVES
t-Norms
Generators of t-Norms
Isomorphisms of t-Norms
Negations
Nilpotent t-Norms and Negations
t-Conorms
DeMorgan Systems
Groups and t-Norms
Interval-Valued Fuzzy Sets
ADDITIONAL TOPICS ON CONNECTIVES
Fuzzy Implications
Averaging Operators
Powers of t-Norms
Sensitivity of Connectives
Copulas and t-Norms
FUZZY RELATIONS
Definitions and Examples
Binary Fuzzy Relations
Operations on Fuzzy Relations
Fuzzy Partitions
Fuzzy Relations as Chu Spaces
UNIVERSAL APPROXIMATION
Fuzzy Rule Bases
Design Methodologies
Some Mathematical Background
Approximation Capability
POSSIBILITY THEORY
Additive and Non-Additive Set Functions
Possibility
Possibility Theory Based on Fuzzy Sets
Approximate Reasoning
Approximate Reasoning in Expert Systems
A Simple Form of Generalized Modus Ponens
The Compositional Rule of Inference
PARTIAL KNOWLEDGE
Incomplete Probabilistic Information
Belief Functions
Reasoning with Belief Functions
Decision Making Using Belief Functions
Rough Sets
Conditional Events
FUZZY MEASURES
Motivation and Definitions
Fuzzy Measures and Lower Probabilities
Fuzzy Measures in Other Areas
Conditional Fuzzy Measures
FUZZY INTEGRALS
Review of the Lebesgue Integral
The Sugeno Integral
The Choquet Integral
The Choquet Integral as a Fuzzy Integral
Radon-Nikodym Derivatives
FUZZY MODELING AND CONTROL
Motivation for Fuzzy Control
The Methodology of Fuzzy Control
Optimal Fuzzy Control
An Analysis of Fuzzy Control Techniques
Plus each chapter includes Exercises
BIBLIOGRAPHY
ANSWERS TO SELECTED EXERCISES
INDEX
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