模糊集合论及其应用 : 第4版

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

Since its inception 20 years ago, the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of this theory can be found, for example, in artificial intelligence, computer science, control engineering, deci-sion theory, expert systems, logic, management science, operations research,pattern recognition, and robotics. Theoretical advances have been made in many directions. In fact it is extremely difficult for a newcomer to the field or for some-body who wants to apply fuzzy set theory to his problems to recognize properly the present "state of the art." Therefore, many applications use fuzzy set theory on a much more elementary level than appropriate and necessary. On the other hand, theoretical publications are already so specialized and assume such a back-ground in fuzzy set theory that they are hard to understand. The more than 4,000 publications that exist in the field are widely scattered over many areas and in many journals. Existing books are edited volumes containing specialized contri-butions or monographs that focus only on specific areas of fuzzy sets, such as pattern recognition [Bezdek 1981], switching functions [Kandel and Lee 1979],or decision making [Kickert 1978]. Even the excellent survey book by Dubois and Prade [1980a] is primarly intended as a research compendium for insiders rather than an introduction to fuzzy set theory or a textbook. This lack of a com-prehensive and modern text is particularly recognized by newcomers to the field and bv those who want to teach fuzzy set theory and its applications.