模糊数学教学学习课件.ppt

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.) II. Introduction of Fuzzy Sets When —— 1965 Who —— L. A. Zadeh (扎德) American computer 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 / Intelligent computer / Artificial intelligence etc. 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,P.N.Marinos发表模糊逻辑的研究报告; 1974年,L.A.Zadeh发表模糊推理的研究报告,从此,模糊理论成了一个热门的课题. 1974年,英国的E.H.Mamdani首次用模糊逻辑和模糊推理实现了世界上第一个实验性的蒸汽机控制,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. 1980年丹麦的L.P.Holmblad和Ostergard在水泥窑炉采用模糊控制并取得了成功,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