文档介绍：FUZZY MATHEMATICS
Copyright © 2010 By Hu Bao Qing
Wuhan University
All rights reserved
Teaching Material
模糊理论基础
胡宝清编著
武汉大学出版社
2004年10月(第二次印刷)
2010年06月(第二版)
I. Science Research Issue
Certainty—— Classical Mathematics
Uncertainty
Stochastic —— Probability & Statistics
Fuzzy —— Fuzzy Math. (Fuzzy Set
Theory / Fuzzy Logic)
(Zadeh, 1965)
Vague —— Rough Sets Theory
(Pawlak, 1982)
Error/Approximative —— Interval Analyses
(Moore, 1966)
Grey —— Grey System Theory (Deng, 1982)
Others (such as Set Pair Analyse, Extenic, etc.)
When —— 1965
Who —— L. A. Zadeh (扎德)
puter & control expert
Now: Professor in the Graduate School, Computer
Science Division, University of California
Before 1965: system theory and decision analysis
After 1965: theory of fuzzy sets and its applications
Where —— Fuzzy Sets, Information and Control 8, 338 –353.
Why —— Uncertainty in control / puter /
Artificial intelligence etc.
/~zadeh/
II. Introduction of Fuzzy Sets
III. Development of Fuzzy Maths
First Stage: Foundation of Basic Theory (1965-1980)
Second Stage: Logic and Inference (1980-1990)
Third Stage: Applications (1990- )
1966年,;
1974年,,从此,模糊理论成了一个热门的课题.
1974年,,并取得了比传统的直接数字控制算法更好的效果,从而宣告模糊控制的诞生.
,这是第一个商业化的有实际意义的模糊控制器.
IV. Fuzzy Maths in China
Threshold —— the second half of 1970’s
Prosperity —— 1980’s
World leading in Fuzzy topology and algebra
Fuzzy Math (《模糊数学》, 原华中理工大学) has international influence
Downfall —— 1990’s
Cause:
1. Theory Application
2. It is not regarded by mathematician
3. Journal was shifted from Wuhan to Hunan and its name was changed as
Fuzzy System and Mathematics (《模糊系统与数学》)
Prosperity again —— 2000’s
V. Applications of Fuzzy Maths
The word “fuzzy” is perhaps no longer fuzzy to many engineers today.
Control Theory
System Theory
Decision Analysis
Information Searches
Medicine
Biology
…….
e