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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） [Fuzzy Set Theory and Its Applications Fourth Edition] 电子书 下载 mobi epub pdf txt

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所谓模糊概念是指这个概念的外延具有不确定性，或者说它的外延是不清晰的，是模糊的。例如“青年”这个概念，它的内涵我们是清楚的，但是它的外延，即什么样的年龄阶段内的人是青年，恐怕就很难说情楚，因为在“年轻”和“不年轻”之间没有一个确定的边界，这就是一个模糊概念。

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东西不错，希望一直好用。

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东西不错，希望一直好用。

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模糊理论（Fuzzy Theory）是指用到了模糊集合的基本概念或连续隶属度函数的理论。它可分类为模糊数学，模糊系统，不确定性和信息，模糊决策这五个分支，它并不是完全独立的，它们之间有紧密的联系。例如，模糊控制就会用到模糊数学和模糊逻辑中的概念。从实际应用的观点来看，模糊理论的应用大部分集中在模糊系统上，尤其集中在模糊控制上。也有一些模糊专家系统应用于医疗诊断和决策支持。由于模糊理论从理论和实践的角度看仍然是新生事物，所以我们期望，随着模糊领域的成熟，将会出现更多可靠的实际应用。

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其次，模糊性是精确性的对立面，但不能消极地理解模糊性代表的是落后的生产力，恰恰相反，我们在处理客观事物时，经常借助于模糊性。例如，在一个有许多人的房间里，找一位“年老的高个子男人”，这是不难办到的。这里所说的“年老”、“高个子”都是模糊概念，然而我们只要将这些模糊概念经过头脑的分析判断，很快就可以在人群中找到此人。如果我们要求用计算机查询，那么就要把所有人的年龄，身高的具体数据输入计算机，然后我们才可以从人群中找这样的人。

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需要注意的几点：首先，人们在认识模糊性时，是允许有主观性的，也就是说每个人对模糊事物的界限不完全一样，承认一定的主观性是认识模糊性的一个特点。例如，我们让100个人说出“年轻人”的年龄范围，那么我们将得到100个不同的答案。尽管如此，当我们用模糊统计的方法进行分析时，年轻人的年龄界限分布又具有一定的规律性；

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开卷有益处,不忘送书人

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知识是人类在实践中认识客观世界的成果。它可能包括事实，信息，描述或在教育和实践中获得的技能。它可能是关于理论的，也可能是关于实践的。在哲学中，关于知识的研究叫做认识论。知识的获取涉及到许多复杂的过程：感觉，交流，推理。知识也可以看成构成人类智慧的最根本的因素。

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