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Fuzzy Set Theory-and Its Applications, Fourth Edition

Fuzzy

Theory

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Fuzzy Set Theory-and Its Applications, Fourth Edition

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Fuzzy Set

Theory-and

Its

Applications, Fourth Edition

Fuzzy

Set

Theory-

and

Its

Applications

Fourth Edition

H.-J. Zimmermann

Springer

Science+Business

Media,

LLC

Library

Congress Cataloging-in-Publication

Data

Zimmermann, H.-J. (Hans-Jiirgen), 1934-

Fuzzy set theory--and its applieations / H.-J. Zimmermann.--4th ed.

p. em.

Includes bibliographieal referenees and index.

ISBN 978-94-010-3870-6 ISBN 978-94-010-0646-0 (eBook)

DOI 10.1007/978-94-010-0646-0

Fuzzy sets. 2. Operations researeh.

Title.

QA248 .Z55 2001

511.3'22--de21

2001

Springer

Seience+Business

Media

New

York

OriginalIy

published

Kluwer

Academic

Publishers

2001

Softcover

reprint

ofthe

hardcover

4th

edition

2001

2001038123

AlI

rights

reserved.

part

ofthis

publication

may

reproduced,

stored

retrieval

system

transmitted

any

form

any

means,

mechanical,

photocopying,

recording,

otherwise,

without

the

prior

written

permission

the

publisher,

Springer

Science+Business

Media,

LLC

Printed

acid-free pa per.

Contents

List of Figures

List of Tables

xiii

Foreword

Preface

xvii

Preface to the Fourth Edition

xix

1 Introduction to Fuzzy Sets

1.1 Crispness , Vagueness, Fuzziness, Uncertainty

1.2 Fuzzy Set Theory

Part I: Fuzzy Mathematics

Fuzzy

Sets-Basic

Definitions

2.1 Basic Definitions

2.2 Basic Set-Theoretic Operations for Fuzzy Sets

3 Extensions

3.1

Types of Fuzzy Sets

3.2 Further Operations on Fuzzy Sets

3.2.1 Algebraic Operations

3.2.2 Set-Theoretic Operations

3.2.3

Criteria for Selecting Appropriate Aggregation Operators

4 Fuzzy Measures and Measures of Fuzziness

4.1 Fuzzy Measures

4.2 Measures of Fuzziness

5 The Extension Principle and Applications

5.1

The Extension Principle

5.2 Operations for Type 2 Fuzzy Sets

5.3 Algebraic Operations with Fuzzy Numbers

5.3.1

Special Extended Operations

5.3.2

Extended Operations for LR-Representation of Fuzzy Sets

vi CONTENTS

Fuzzy Relations and Fuzzy Graphs 71

6.1

Fuzzy Relations on Sets and Fuzzy Sets

6.1.1

Compositions of Fuzzy Relations 76

6.1.2

Properties of the Min-Max Composition 79

6.2

Fuzzy Graphs

6.3

Special Fuzzy Relations

Fuzzy Analysis

7.1

Fuzzy Functions on Fuzzy Sets

7.2

Extrema of Fuzzy Functions

7.3

Integration of Fuzzy Functions

7.3.1

Integration of a Fuzzy Function over a Crisp Interval 100

7.3.2

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

Interval

103

7.4

Fuzzy Differentiation

107

Uncertainty Modeling

111

8.1

Application-oriented Modeling of Uncertainty

111

8.1.1 Causes of Uncertainty 114

8.1.2

Type of Available Information 117

8.1.3

Uncertainty Methods 118

8.1.4

Uncertainty Theories as Transformers of Information 119

8.1.5

Matching Uncertainty Theory and Uncertain Phenomena 120

8.2

Possibility Theory 122

8.2.1

Fuzzy Sets and Possibility Distributions

122

8.2.2

Possibility and Necessity Measures 126

8.3

Probability of Fuzzy Events 129

8.3.1

Probability of a Fuzzy Event as a Scalar 129

8.3.2

Probability of a Fuzzy Event as a Fuzzy Set

131

8.4

Possibility vs. Probability 133

Part II: Applications of Fuzzy Set Theory 139

Fuzzy Logic and Approximate Reasoning

141

9.1 Linguistic Variables 141

9.2

Fuzzy Logic 149

9.2.1

Classical Logics Revisited 149

9.2.2

Linguistic Truth Tables

153

9.3

Approximate and Plausible Reasoning 156

9.4

Fuzzy Languages 160

9.5

Support Logic Programming and Fril

169

9.5.1

Introduction 169

9.5.2

Fril Rules 170

9.5.3

Inference Methods in Fril

172

9.5.4

Fril Inference for a Single Rule 175

9.5.5

Multiple Rule Case 176

9.5.6

Interval and Point Semantic Unification

177

9.5.7

Least Prejudiced Distribution and Learning 179

9.5.8

Applications of Fril

181

剩余524页未读，继续阅读

Set theory and logic.pdf

#ifdef fuzzy_pid_rule_base_deep_copy for (unsigned int j = 0; j < 4 * qf_default; ++j) { fuzzy_struct->mf_params[j] = mf_params[j]; } for (unsigned int k = 0; k < fuzzy_struct->output_num * qf_default; ++k) { for (unsigned int i = 0; i < qf_default; ++i) { fuzzy_struct->rule_base[k * 7 + i] = rule_base[k][i]; } } #else fuzzy_struct->mf_params = mf_params; fuzzy_struct->rule_base = (int *) rule_base; #endif fuzzy_struct->fo_type = fo_type; fuzzy_struct->df_type = df_type; } 分析、

这段代码包含一个条件编译指令 `#ifdef fuzzy_pid_rule_base_deep_copy` 和一个对应的条件编译结束指令 `#endif`。这个指令的作用是根据编译时的宏定义来选择不同的代码执行路径。当 `fuzzy_pid_rule_base_deep_...

void fuzzy_params_init(struct fuzzy *fuzzy_struct, unsigned int mf_type, unsigned int fo_type, unsigned int df_type, int mf_params[], int rule_base[][qf_default]) { for (unsigned int i = 0; i < fuzzy_struct->input_num + fuzzy_struct->output_num; ++i) { fuzzy_struct->mf_type[i] = mf_type; } for (unsigned int i = 0; i < fuzzy_struct->output_num; ++i) { fuzzy_struct->output[i] = 0; } 分析

这段代码定义了一个名为 `fuzzy_params_init` 的函数，它的参数包括一个指向 `struct fuzzy` 类型的指针 `fuzzy_struct`，三个无符号整数 `mf_type`、`fo_type` 和 `df_type`，一个整型数组 `mf_params`，和一个二维...

void delete_fuzzy(struct fuzzy *fuzzy_struct) { free(fuzzy_struct->mf_type); free(fuzzy_struct->output); free(fuzzy_struct); } 分析这段

这段代码定义了一个名为 `delete_fuzzy` 的函数，它的参数是一个指向 `struct fuzzy` 类型的指针 `fuzzy_struct`。函数的作用是释放 `fuzzy_struct` 所指向的结构体及其成员变量所占用的内存空间。具体来说，它依次...

解释 e = set - DATE; //目标值 - 实际值 ec = e - lastE; //误差变化率 sumE += e; lastE = e; if (set > 2) { OUT = fuzzy(e, ec);

最后，如果目标值 set 大于 2，调用 fuzzy 函数来计算 PID 控制器的输出值 OUT。其中，e 和 ec 是 fuzzy 函数的输入参数，表示当前误差和误差变化率；OUT 是 fuzzy 函数的返回值，表示 PID 控制器的输出值，即比例、...

fuzzy C-means clustering）算法对数据进行聚类python

在Python中，我们可以使用scikit-learn库来实现模糊C均值（fuzzy C-means clustering）算法。以下是一个简单的示例代码：首先，我们需要导入必要的库： ```python from sklearn.cluster import KMeans from ...

anfis怎么预测python

ANFIS（Adaptive Neuro-Fuzzy Inference System）是一种基于神经网络和模糊逻辑的混合模型，用于建立输入和输出之间的非线性映射关系。在Python中，可以使用Python的Scikit-Fuzzy和Neuro-Fuzzy库来实现ANFIS模型。 ...

fuzzy Classifier在哪些包里可以导入

Fuzzy Classifier是一种基于模糊逻辑的分类器，常常应用于模糊控制、数据挖掘和机器学习等领域。在Python中，可以使用以下几个包来导入Fuzzy Classifier： 1. scikit-fuzzy：scikit-fuzzy是一个基于NumPy和SciPy的...

优化代码达成当set大于0.5时OUT = fuzzy(e, ec); 当set小于0.5时out=set的目的，代码如下：int speed_pid() { int e = -1,ec = -2.6; static PID pid= {0.02, 0.3, 0}; //赋予初值 static int sumE = 0; //累加偏差 static int lastE = 0; PID OUT = {0, 0, 0}; e = set - DATE; //目标值-实际值 ec = e - lastE; //误差变化率 sumE += e; lastE = e; OUT = fuzzy(e, ec); //模糊控制调整 return (pid.Kp+OUT.Kp)e + (pid.Kd+OUT.Kd)ec + (pid.Ki+OUT.Ki)*sumE; }

您提供的代码并没有达成当set大于0.5时OUT = fuzzy(e, ec); 当set小于0.5时out=set的目的。如果要实现该目的，可以在计算OUT之前加上一个判断语句，如下所示： ```c++ if (set > 0.5) { OUT = fuzzy(e, ec); } ...

美国地图json文件，可以使用arcgis转为spacefile

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Fuzzy Set Theory-and Its Applications, Fourth Edition

Set theory and logic.pdf

void delete_fuzzy(struct fuzzy *fuzzy_struct) { free(fuzzy_struct->mf_type); free(fuzzy_struct->output); free(fuzzy_struct); } 分析这段

可以介绍一下什么是𝑞-Rung orthopair fuzzy set 和 mass assignment吗？以及它们的应用

二十篇有关直觉模糊集的文献综述

生成基于模糊集理论的图像增强算法的MATLAB代码

请谈谈k-means, EM, fuzzy c-means算法异同。

fuzzy c-means

编写python代码，实现将一列数据变成一个直觉模糊集

Fuzzy C-means算法怎么实现

A Centroid Auto-Fused Hierarchical Fuzzy c-Means Clustering的更新结构图可以给出吗

Possibilistic Fuzzy c-Means Clustering python代码

那怎么用中文翻译𝑞-Rung orthopair fuzzy set 和 mass assignment

解释 e = set - DATE; //目标值 - 实际值 ec = e - lastE; //误差变化率 sumE += e; lastE = e; if (set > 2) { OUT = fuzzy(e, ec);

fuzzy C-means clustering）算法对数据进行聚类python

anfis怎么预测python

fuzzy Classifier在哪些包里可以导入

美国地图json文件，可以使用arcgis转为spacefile

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