模糊数学英文版ppt

1、-JEvorFUZZY MATHEMATICSCopyright © 2010 By Hu Bao QingWuhan UniversityAll rights reserved创.Y阻a Teaching Material、2模糊理论基础胡宝清编著武汉大学出版社5理论与工程系列丛书 / 2004年10月（第二次印刷）2010年06月（第二版）©仝31优齐出版社 武汉大学出版社II理论基础胡宝清编著AVagueI. Science Research Issue CertaintyClassical Mathematics UncertaintyStochasticProba

2、bility & StatisticsFuzzy Fuzzy Math. (Fuzzy SetTheory / Fuzzy Logic)(Zadeh, 1965)Rough Sets Theory (Pawlak, 1982)Error/ApproximativeInterval Analyses(Moore, 1966)GreyGrey System Theory (Deng, 198Others (such as Set Pair Analyse, Exten etc.) i山心 cjkiacL 2, 3L£p53 UJ65；Fuzzy Sets*L. A. ZadehD

3、eparhnent of Electrical Engineering and Electronics Research LaboratoryUniwrty of California Berkeley, CaliforniaA fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of m

4、embership ranging between zero and one The notions of inclusion, union, intersection, complement, relation, convexity, etc.j are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is p

5、roved without requiring that the fuz为y sets be disjoint.L INTRODUCTIONIII. 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JP.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，

6、从此，模 二 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O stergard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. Thresholdthe second half of 19701 Prosperity 1980' sWorld leading in Fuzzy topology and algebraFuzzy Math （模糊数

7、学，原华中理工大学） has international influenceDownfall19901Cause:» Application1. Theory < disjoint2. It is not regarded by mathematician3. Journal was shifted from Wuhan to Hunanand its name was changed asFuzzy System and Mathematics （模糊系统与数学）Prosperity again200（TsV. Applications of Fuzzy MathsThe w

8、ord "fuzzy" is perhaps no longer fuzzy to many engineers today. Control Theory System Theory Decision Analysis Information Searches MedicineBiologyg Household Electrical WaresFuzzy Water HeaterFuzzy Electric CookerFuzzy Air-conditionerFuzzy WasherFuzzy CleanerFuzzy RefrigeratorFuzzy Microw

9、ave OvenFuzzy Colour TV SetFuzzy Electric Fane.g. Fuzzy Washergrade(of membership)e.g. Fuzzy Washergrade (oi membership)1.MediumVeryShortShortLongVeryLong38.88washtime minute68.08e.g. Fuzzy Washere.g. Fuzzy Electric Fan看一则广告 电风扇系列落地扇原产地：中国三公司：广东祥立实业有限公司（国际销售 部）五星级供应商会员流畅时尚外观模糊逻辑控制技术谨 细信息三 Vie Benefi

10、ts of Fuzzy Mathematics The ability to model highly complex business problemsStephen Making （斯蒂芬.霍金）二2000年指出我认为，下个世纪将是复杂性的世纪(I think the next century will be thecentury of complexity）4 珂 Improved cognitive modeling of expert system 二What makes an expert an expert? With their ability to directly mode

11、l such imprecise information, fuzzy systems reduce overall cognitive dissonance （不一致）in the modeling processThe ability to model systems involving multiple experts二 Fuzzy systems are well suited to representing multiple cooperating, collaborating, and even conflicting experts.rAHReduced model comple

12、xityFuzzy models, as we will see, require fewer rules than conventional system, and these rules are closer to the way knowledge is expressed in natural language. Improved handling of uncertainty and possibilitiesThe representation of uncertainty in expert and decision support systems is an area of c

13、ontinual debate. In this aspect, fuzzy logic provides a better, more consistent, and more mathematically sound method of handling uncertainties j. 厂 H 一 VII. Naive Thoughts on Fuzzy二g 2 e V.y / / Lr芒;济決碎诗处沐 厂:Fuzzy phenomena and fuzzy conceptse.g. ram is a nature phenomenon.mizzle downpoure 臥 H rg X

14、 I :u洱； 鸞f h :悴 / 气存A虚三e.g.l电脑不如人脑Fuzzy partition： light rain, moderate rain, heavy rain比如，解释“大雨”，专业的天气预报书籍可能解释 C 为“二十四小时内雨量累计(在雨量收集器内)达 40至79.9毫米(mm)雨”，这是十分精确的。Fuzzy inference* predicting a good, fair, or poorharvest this year based on the results offuzzy judging.两岁的小孩图像识别能力语音识别能力Science 三操作电脑猴子可通过

15、思维代替“手”e.g. 2 “请你十点左右在行政大楼附近等我一WhereWhen三 Examples on fuzzy conceptsConi(tneiollowins statements三Theenginetemperature is 二 hot.sExamples on fuzzy conceptsExamples on fuzzy conceptssExamples on fuzzy conceptsExamples on fuzzy conceptsCurrent inflation rates arerising rapidly>Current inflation rate

16、s are rising rapidly.二 1CPI消费者价格指数PPI生产者价格指数二 ii PExamples on fuzzy conceptsTom is rather talk but Judy is short.If you are tall, than you are quite likely heavy.hf rhaThe description of a human characteristic such as hecMiy.The classification of patients as depressed.The classification of certain o

17、bjects as large.The classification of people by age such as old.A rule for driving such as "if an obstacle is close, then brake immediately".Examples on fuzzy concepts如果有一天我们能建立法律公式F（X,无，X”）=甲eaiaitg months of下隔、失业imprisonmentconcept.a.all of the objects defined byConcept and setintension

18、(内涵)：attributes of the objectG. Cantor (1887)：A-aPa)If a fuzzy concept can be rigidly describedCantoris notion of sets or the bivalent(true/false or two-valued) logic ?=模糊概念能否用Cantor集合来刻画？秃头悖论一位已经谢顶的老教授与他的学生争论他是否为秃头问题。1教授：我是秃头吗？Y生：您的头顶上已经没有多少头发，确实应该说是。-色授：你秀发稠密，绝对不算秃头，问你，如果你头上脱落了一根头发之后，- 能说变成了秃头了吗？学生：我减少一根头发之后，当然不会变成秃头。教授：好了，总结我们的讨论，得出下面的命题：。如果一个人不是秃头，那 么他减少一根头发仍不是秃头'，你说对吗？；学生：对！鹫授：我年轻时代也和你一样一头秀发，当时没有人说我秃头，后来随着年龄 £°的增高，头发一根根减少到今天的样子。但每掉一根头发，根据我们刚 才的命题，我都不应该称为秃头，这样经有限次头发的减少，醛-命 暨竅右限次,结论是：戟今天仍不是秃头，。Postulate: If a man with n (a n