《模糊集合论及其应用(第4版)》旨在为模糊理论方面的学者提供一部入门级教程，不仅满足了学生学习的需要，也很适合相关的专家学习深入研究。为了使本书不仅仅是一部初级教程，读者范围更加广泛，增加了许多参考资料。知识体系新颖，时代气息十足，不仅是对模糊理论的最现代解释，也很适合学习该理论的应用技巧。本书由齐默尔曼编。

List of Figures

List of Tables

Foreword

Preface

Preface to the Fourth Edition

Introduction to Fuzzy Sets

Crispness, Vagueness, Fuzziness, Uncertainty

Fuzzy Set Theory

Fuzzy Mathematics

Fuzzy Sets-Basic Definitions

Basic Definitions

Basic Set-Theoretic Operations for Fuzzy Sets

Extensions

Types of Fuzzy Sets

Further Operations on Fuzzy Sets

Algebraic Operations

Set-Theoretic Operations

Criteria for Selecting Appropriate Aggregation Operators

Fuzzy Measures and Measures of Fuzziness

Fuzzy Measures

Measures of Fuzziness

The Extension Principle and Applications

The Extension Principle

Operations for Type 2 Fuzzy Sets

Algebraic Operations with Fuzzy Numbers

Special Extended Operations

Extended Operations for LR-Representation of Fuzzy Sets

Fuzzy Relations and Fuzzy Graphs

Fuzzy Relations on Sets and Fuzzy Sets

Compositions of Fuzzy Relations

Properties of the Min-Max Composition

Fuzzy Graphs

Special Fuzzy Relations

Fuzzy Analysis

Fuzzy Functions on Fuzzy Sets

Extrema of Fuzzy Functions

Integration of Fuzzy Functions

Integration of a Fuzzy Function over a Crisp Interval

Integration of a （Crisp） Real-Valued Function over a Fuzzy

Interval

Fuzzy Differentiation

Uncertainty Modeling

Application-oriented Modeling of Uncertainty

Causes of Uncertainty

Type of Available Information

Uncertainty Methods

Uncertainty Theories as Transformers of Information

Matching Uncertainty Theory and Uncertain Phenomena

Possibility Theory

Fuzzy Sets and Possibility Distributions

Possibility and Necessity Measures

Probability of Fuzzy Events

Probability of a Fuzzy Event as a Scalar

Probability of a Fuzzy Event as a Fuzzy Set

Possibility vs. Probability

Applications of Fuzzy Set Theory

Fuzzy Logic and Approximate Reasoning

Linguistic Variables

Fuzzy Logic

Classical Logics Revisited

Linguistic Truth "rabies

Approximate and Plausible Reasoning

Fuzzy Languages

Support Logic Programming and Fril

Introduction

Fril Rules

Inference Methods in Fril

FrU Inference for a Single Rule

Multiple Rule Case

Interval and Point Semantic Unification

Least Prejudiced Distribution and Learning

Applications of Fril

Fuzzy Sets and Expert Systems

Fuzzy Control

Fuzzy Data Bases and Queries

Fuzzy Data Analysis

Decision Making In Fuzzy Environments

Applications of Fuzzy Sets in Engineering and Management

Empirical Research in Fuzzy Set Theory

Future Perspectives