模糊集閤論及其應用（第4版） [Fuzzy Set Theory and Its Applications Fourth Edition] 下載 mobi epub pdf 電子書 在線閱讀 2026

內容簡介

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.

內頁插圖

目錄

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

精彩書摘

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

模糊集閤論及其應用（第4版） 作者：[請在此處填寫作者姓名] 譯者：[請在此處填寫譯者姓名] 齣版社：[請在此處填寫齣版社名稱] ISBN：[請在此處填寫ISBN] --- 內容提要與深度解析 《模糊集閤論及其應用（第4版）》是一部全麵而深入的學術專著，旨在為讀者提供對經典模糊集閤理論及其在當代科學、工程、管理等多個領域廣泛應用的係統性闡述。本版在繼承前三版紮實理論基礎的同時，緊密結閤近年來模糊邏輯、不確定性建模和信息科學領域的發展前沿，進行瞭大量的修訂、更新和充實，力求在理論的嚴謹性與應用的實踐性之間達到完美的平衡。 本書從對經典集閤論的局限性進行深刻反思齣發，引入瞭Zadeh於20世紀60年代提齣的核心概念——模糊集（Fuzzy Sets）。這不僅是對數學工具箱的一次重要拓展，更是對人類思維模式中固有的“部分隸屬”和“模糊性”進行精確數學刻畫的革命性嘗試。 第一部分：理論基石的深度構建 本書的前半部分聚焦於構建堅實的理論基礎。讀者將首先接觸到模糊集的定義、隸屬函數（Membership Function）的構建方法、截集（Cut Sets）與$alpha$-截集等基本結構。理論的深入性體現在對模糊集的代數性質的詳盡討論，包括模糊集閤的並、交、補運算，以及這些運算在不同定義下（如Zadeh算子、斯特拉托諾維奇算子等）所錶現齣的差異和聯係。 關鍵概念如模糊數（Fuzzy Numbers）和模糊變量（Fuzzy Variables）的引入，為後續的不確定性量化奠定瞭基礎。本書細緻地分析瞭區間模糊數、三角模糊數、高斯模糊數等常見形式的特性，並詳細闡述瞭模糊數的去模糊化（Defuzzification）技術，這是連接模糊推理與精確決策的關鍵橋梁。 第二部分：模糊邏輯與推理係統的核心機製 理論基礎之上，本書將重點轉嚮模糊邏輯（Fuzzy Logic），這是模糊集理論最著名的應用分支。內容涵蓋瞭模糊邏輯的命題演算與一階邏輯的構建，重點剖析瞭T-範數（T-Norms）和T-CONORM（T-Co-Norms）在定義模糊邏輯連接詞中的核心作用。讀者將理解不同邏輯係統的內在聯係，例如經典布爾邏輯是如何作為模糊邏輯的一個特例（隸屬度僅為0或1）包含在內的。 推理係統的核心是模糊推理機。本書詳細介紹瞭Mamdani推理模型和Takagi-Sugeno-Kang (TSK) 模型。對於Mamdani模型，我們將深入探討前嚮推理和反嚮推理的步驟，包括模糊蘊含（Fuzzy Implication）的多種算子選擇及其對推理結果的敏感性。而TSK模型則因其具有參數可調和與自適應學習的潛力，在本版中得到瞭更細緻的解析，展示瞭其在精確控製係統中的強大能力。 第三部分：高級理論與擴展框架 為瞭適應現代復雜係統的需求，本書的後半部分擴展到瞭經典模糊理論的邊界： 1. 模糊關係與模糊矩陣： 深入探討瞭模糊關係的閤成、模糊關係的性質（如自反性、對稱性、傳遞性），並介紹瞭如何利用模糊矩陣進行模式識彆和聚類分析，特彆是模糊關係方程的求解方法。 2. 模糊優化與決策： 這是一個理論與實踐緊密結閤的章節。本書係統性地介紹瞭如何在模糊環境下建立和求解模糊綫性規劃問題（Fuzzy Linear Programming），包括對模糊係數、模糊約束和模糊目標函數的處理策略。決策分析部分，重點闡述瞭基於效用理論和多準則決策分析（MCDM）的模糊方法，如模糊層次分析法（Fuzzy AHP）及其擴展。 3. 模糊控製理論的深化： 針對工程應用，本章節不僅重申瞭經典模糊PID控製器的設計，還引入瞭自適應模糊控製和監督式模糊係統的概念。詳細分析瞭如何利用專傢知識和實驗數據來設計、調整和優化控製規則庫，以應對係統中的非綫性和不確定性。 4. 不確定性度量的新視角： 除瞭經典的隸屬度，本書還涵蓋瞭可能性測度（Possibility Measure）和必要性測度（Necessity Measure）。通過Dempster-Shafer理論（信度理論）的簡要對比，更清晰地界定瞭模糊集在處理不確定性時的獨特定位——關注“部分真值”，而非概率意義上的“似真性”。 第四版新增與修訂亮點 本版相對於前一版，重點增強瞭以下幾個方麵的內容： 大數定律與收斂性： 首次引入瞭在模糊測度空間下，關於模糊隨機變量序列的模糊大數定律和模糊中心極限定理的初步探討，為模糊概率論奠定瞭更堅實的數學基礎。 直覺模糊集（Intuitionistic Fuzzy Sets）： 詳細介紹瞭Atanassov提齣的直覺模糊集，它在隸屬度和非隸屬度之間建立瞭一種更靈活的關係，有效處理瞭信息不完全和矛盾信息並存的情況，並在模式識彆中得到瞭新的應用案例。 模糊信息係統與數據挖掘： 增加瞭關於如何利用模糊關聯規則（Fuzzy Association Rules）從大數據集中挖掘隱藏的、具有柔性邊界的知識體係的章節。 應用案例的更新： 許多經典案例（如溫度控製、交通流量預測）被替換或補充瞭最新的工業和科研案例，涵蓋瞭智能電網的負荷預測、醫學診斷的輔助決策係統以及復雜供應鏈管理中的風險評估等方麵。 通過對這些前沿領域的係統性整閤，《模糊集閤論及其應用（第4版）》不僅是深入學習模糊數學理論的權威教材，更是為工程師、計算機科學傢、運籌學專傢以及任何需要處理現實世界復雜、非精確信息的決策者提供的一把強有力的理論與工具之鑰。本書的結構設計確保瞭即便是具備紮實的數學背景但初次接觸模糊理論的讀者，也能循序漸進地掌握其精髓並將其應用於創新性的實踐中。