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a course in fuzzy systems and control

模糊控制

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a course in fuzzy systems and control; 王立新，模糊控制经典教程，英文原版

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COURSE

IN'FUZZY

Li-Xin

Wang

Course

Fuzzy

Systems

and

Control

Li-Xin Wang

Prentice-Hall International, Inc.

Contents

Preface

Introduction

1.1

Why Fuzzy Systems?

1.2 What Are Fuzzy Systems?

1.3 Where Are

Fuzzy Systems Used and How?

1.3.1 Fuzzy Washing Machines

1.3.2 Digital Image Stabilizer

1.3.3 Fuzzy Systems in Cars

1.3.4 Fuzzy Control of

Cement Kiln

1.3.5

Fuzzy Control of Subway Train

1.4 What Are the Major Research Fields in Fuzzy Theory?

1.5

Brief History of Fuzzy Theory and Applications

1.5.1 The 1960s: The Beginning of Fuzzy Theory

1.5.2 The 1970s: Theory Continued to Grow and Real Applications

Appeared

1.5.3 The 1980s: Massive Applications Made a Difference

1.5.4 The 1990s: More Challenges Remain

1.6 Summary and Further Readings

1.7 Exercises

The Mathematics of

Fuzzy

Systems and Control

Fuzzy

Sets and Basic Operations on

Fuzzy

Sets

2.1

From Classical Sets to Fuzzy Sets

2.2

Basic Concepts Associated with Fuzzy Set

Contents

2.3

Operations on Fuzzy Sets

2.4

Summary and Further Readings

2.5

Exercises

Further Operations on Fuzzy Sets

3.1

Fuzzy Complement

3.2

Fuzzy Union-The S-Norms

3.3

Fuzzy Intersection-The T-Norms

3.4

Averaging Operators

3.5

Summary and Further Readings

3.6

Exercises

Fuzzy Relations and the Extension Principle

4.1

From Classical Relations to Fuzzy Relations

4.1.1

Relations

4.1.2

Projections and Cylindric Extensions

4.2

Compositions of Fuzzy Relations

4.3

The Extension Principle

4.4

Summary and Further Readings

4.5

Exercises

Linguistic Variables and Fuzzy IF-THEN Rules

5.1

From Numerical Variables to Linguistic Variables

5.2

Linguistic Hedges

5.3

Fuzzy IF-THEN Rules

5.3.1

Fuzzy Propositions

5.3.2

Interpretations of Fuzzy IF-THEN Rules

5.4

Summary and Further Readings

5.5

Exercises

Fuzzy Logic and Approximate Reasoning

6.1

From Classical Logic to Fuzzy Logic

6.1.1

Short Primer on Classical Logic

6.1.2

Basic Principles in Fuzzy Logic

6.2

The Compositional Rule of Inference

6.3

Properties of the Implication Rules

6.3.1

Generalized Modus Ponens

6.3.2

Generalized Modus Tollens

CONTENTS

6.3.3 Generalized Hypothetical Syllogism

6.4 Summary and Further Readings

6.5 Exercises

Fuzzy Systems

and

Their Properties

Fuzzy Rule Base and Fuzzy Inference Engine

7.1 Fuzzy Rule Base

7.1.1

Structure of Fuzzy Rule Base

7.1.2 Properties of Set of Rules

7.2 Fuzzy Inference Engine

7.2.1 Composition Based Inference

7.2.2 Individual-Rule Based Inference

7.2.3

The Details of Some Inference Engines

7.3 Summary and Further Readings

7.4 Exercises

Fuzzifiers and Defuzzifiers

8.1 Fuzzifiers

8.2 Defuzzifiers

8.2.1 center of gravity Defuzzifier

8.2.2 Center Average Defuzzifier

8.2.3 Maximum Defuzzifier

8.2.4 Comparison of the Defuzzifiers

8.3 Summary and Further Readings

8.4 Exercises

Fuzzy Systems as Nonlinear Mappings

9.1 The Formulas of Some Classes of Fuzzy Systems

9.1.1

Fuzzy Systems with Center Average Defuzzifier

9.1.2

Fuzzy Systems with Maximum Defuzzifier

9.2

Fuzzy Systems As Universal Approximators

9.3 Summary and Further Readings

9.4 Exercises

10 Approximation Properties of Fuzzy Systems

10.1 Preliminary Concepts

10.2 Design of Fuzzy System

vii

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