模糊集合论及其应用（第4版） [Fuzzy Set Theory and Its Applications Fourth Edition] pdf epub mobi txt 电子书 下载 在线阅读 2026

内容简介

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.

内页插图

目录

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

精彩书摘

situation and is meant to be a mapping of a problem, a system, or a process. In contrast to a scientific theory, containing scientific laws as hypotheses, a model normally does not assert invariance with respect to time and space but requires modifications whenever the specific context for which the model was constructed changes.
In the following, we will concentrate on models rather than on theories. Real-izing that there is quite a variety of types of models, we do not think that it is important and necessary for our purposes to distinguish models by their language （mathematics or logic is considered to be a modeling language）, by area, by problem type, by size, and so on. One classification, however, seems to be impor-tant: the distinction of models by their character. Scientific theories were already divided into formal theories and factual theories.
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前言/序言

模糊集合论及其应用（第4版） 作者：[请在此处填写作者姓名] 译者：[请在此处填写译者姓名] 出版社：[请在此处填写出版社名称] ISBN：[请在此处填写ISBN] --- 内容提要与深度解析 《模糊集合论及其应用（第4版）》是一部全面而深入的学术专著，旨在为读者提供对经典模糊集合理论及其在当代科学、工程、管理等多个领域广泛应用的系统性阐述。本版在继承前三版扎实理论基础的同时，紧密结合近年来模糊逻辑、不确定性建模和信息科学领域的发展前沿，进行了大量的修订、更新和充实，力求在理论的严谨性与应用的实践性之间达到完美的平衡。 本书从对经典集合论的局限性进行深刻反思出发，引入了Zadeh于20世纪60年代提出的核心概念——模糊集（Fuzzy Sets）。这不仅是对数学工具箱的一次重要拓展，更是对人类思维模式中固有的“部分隶属”和“模糊性”进行精确数学刻画的革命性尝试。 第一部分：理论基石的深度构建 本书的前半部分聚焦于构建坚实的理论基础。读者将首先接触到模糊集的定义、隶属函数（Membership Function）的构建方法、截集（Cut Sets）与$alpha$-截集等基本结构。理论的深入性体现在对模糊集的代数性质的详尽讨论，包括模糊集合的并、交、补运算，以及这些运算在不同定义下（如Zadeh算子、斯特拉托诺维奇算子等）所表现出的差异和联系。 关键概念如模糊数（Fuzzy Numbers）和模糊变量（Fuzzy Variables）的引入，为后续的不确定性量化奠定了基础。本书细致地分析了区间模糊数、三角模糊数、高斯模糊数等常见形式的特性，并详细阐述了模糊数的去模糊化（Defuzzification）技术，这是连接模糊推理与精确决策的关键桥梁。 第二部分：模糊逻辑与推理系统的核心机制 理论基础之上，本书将重点转向模糊逻辑（Fuzzy Logic），这是模糊集理论最著名的应用分支。内容涵盖了模糊逻辑的命题演算与一阶逻辑的构建，重点剖析了T-范数（T-Norms）和T-CONORM（T-Co-Norms）在定义模糊逻辑连接词中的核心作用。读者将理解不同逻辑系统的内在联系，例如经典布尔逻辑是如何作为模糊逻辑的一个特例（隶属度仅为0或1）包含在内的。 推理系统的核心是模糊推理机。本书详细介绍了Mamdani推理模型和Takagi-Sugeno-Kang (TSK) 模型。对于Mamdani模型，我们将深入探讨前向推理和反向推理的步骤，包括模糊蕴含（Fuzzy Implication）的多种算子选择及其对推理结果的敏感性。而TSK模型则因其具有参数可调和与自适应学习的潜力，在本版中得到了更细致的解析，展示了其在精确控制系统中的强大能力。 第三部分：高级理论与扩展框架 为了适应现代复杂系统的需求，本书的后半部分扩展到了经典模糊理论的边界： 1. 模糊关系与模糊矩阵： 深入探讨了模糊关系的合成、模糊关系的性质（如自反性、对称性、传递性），并介绍了如何利用模糊矩阵进行模式识别和聚类分析，特别是模糊关系方程的求解方法。 2. 模糊优化与决策： 这是一个理论与实践紧密结合的章节。本书系统性地介绍了如何在模糊环境下建立和求解模糊线性规划问题（Fuzzy Linear Programming），包括对模糊系数、模糊约束和模糊目标函数的处理策略。决策分析部分，重点阐述了基于效用理论和多准则决策分析（MCDM）的模糊方法，如模糊层次分析法（Fuzzy AHP）及其扩展。 3. 模糊控制理论的深化： 针对工程应用，本章节不仅重申了经典模糊PID控制器的设计，还引入了自适应模糊控制和监督式模糊系统的概念。详细分析了如何利用专家知识和实验数据来设计、调整和优化控制规则库，以应对系统中的非线性和不确定性。 4. 不确定性度量的新视角： 除了经典的隶属度，本书还涵盖了可能性测度（Possibility Measure）和必要性测度（Necessity Measure）。通过Dempster-Shafer理论（信度理论）的简要对比，更清晰地界定了模糊集在处理不确定性时的独特定位——关注“部分真值”，而非概率意义上的“似真性”。 第四版新增与修订亮点 本版相对于前一版，重点增强了以下几个方面的内容： 大数定律与收敛性： 首次引入了在模糊测度空间下，关于模糊随机变量序列的模糊大数定律和模糊中心极限定理的初步探讨，为模糊概率论奠定了更坚实的数学基础。 直觉模糊集（Intuitionistic Fuzzy Sets）： 详细介绍了Atanassov提出的直觉模糊集，它在隶属度和非隶属度之间建立了一种更灵活的关系，有效处理了信息不完全和矛盾信息并存的情况，并在模式识别中得到了新的应用案例。 模糊信息系统与数据挖掘： 增加了关于如何利用模糊关联规则（Fuzzy Association Rules）从大数据集中挖掘隐藏的、具有柔性边界的知识体系的章节。 应用案例的更新： 许多经典案例（如温度控制、交通流量预测）被替换或补充了最新的工业和科研案例，涵盖了智能电网的负荷预测、医学诊断的辅助决策系统以及复杂供应链管理中的风险评估等方面。 通过对这些前沿领域的系统性整合，《模糊集合论及其应用（第4版）》不仅是深入学习模糊数学理论的权威教材，更是为工程师、计算机科学家、运筹学专家以及任何需要处理现实世界复杂、非精确信息的决策者提供的一把强有力的理论与工具之钥。本书的结构设计确保了即便是具备扎实的数学背景但初次接触模糊理论的读者，也能循序渐进地掌握其精髓并将其应用于创新性的实践中。