模糊數(shù)學(xué)-材料

1、FUZZY MATHEMATICS,Copyright 2010 By Hu Bao Qing Wuhan University All rights reserved,Teaching Material,模糊理論基礎(chǔ) 胡寶清 編著 武漢大學(xué)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 1974年,L.A.Zadeh發(fā)表模糊推理的研究報(bào)告,從此,模糊理論成了一個(gè)熱門的課題. 1974年,英

2、國(guó)的E.H.Mamdani首次用模糊邏輯和模糊推理實(shí)現(xiàn)了世界上第一個(gè)實(shí)驗(yàn)性的蒸汽機(jī)控制,并取得了比傳統(tǒng)的直接數(shù)字控制算法更好的效果,從而宣告模糊控制的誕生. 1980年丹麥的L.P.Holmblad和Ostergard在水泥窯爐采用模糊控制并取得了成功,這是第一個(gè)商業(yè)化的有實(shí)際意義的模糊控制器.,IV. Fuzzy Maths in China,Threshold the second half of 1970s Prosperity 1980s World leading in Fuzzy topology and algebra Fuzzy Math (模糊數(shù)學(xué), 原華中理工大學(xué)) has

3、 international influence,Downfall 1990s 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 (模糊系統(tǒng)與數(shù)學(xué)) Prosperity again 2000s,V. Applications of Fuzzy Maths,The word “fuzzy” is perhaps

4、no longer fuzzy to many engineers today. Control Theory System Theory Decision Analysis Information Searches Medicine Biology .,e.g. Household Electrical Wares,Fuzzy Water Heater Fuzzy Electric Cooker Fuzzy Air-conditioner Fuzzy Washer Fuzzy Cleaner Fuzzy Refrigerator Fuzzy Microwave Oven Fuzzy Colo

5、ur TV Set Fuzzy Electric Fan ,e.g. Fuzzy Washer,These,e.g. Fuzzy Washer,These,e.g. Fuzzy Washer,These,e.g. Fuzzy Electric Fan,看一則廣告,minutes.,These,電風(fēng)扇系列 落地扇 原產(chǎn)地：中國(guó) 公司： 廣東祥立實(shí)業(yè)有限公司（國(guó)際銷售部） 五星級(jí)供應(yīng)商會(huì)員 流暢時(shí)尚外觀 模糊邏輯控制技術(shù). 詳細(xì)信息,高管為什么要他們學(xué)模糊數(shù)學(xué),e.g. 2008年8月應(yīng)邀到深圳為富士康(Foxconn)高層人員講模糊理論36學(xué)時(shí),minutes.,These,VI. Benefi

6、ts of Fuzzy Mathematics,The ability to model highly complex business problems Stephen Haking（斯蒂芬.霍金） 2000年指出 我認(rèn)為，下個(gè)世紀(jì)將是復(fù)雜性的世紀(jì)(I think the next century will be the century of complexity),Improved cognitive modeling of expert system,What makes an expert an expert? With their ability to directly model

7、such imprecise information, fuzzy systems reduce overall cognitive dissonance (不一致) in the modeling process.,The ability to model systems involving multiple experts Fuzzy systems are well suited to representing multiple cooperating, collaborating, and even conflicting experts.,Reduced model complexi

8、ty Fuzzy 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 possibilities The representation of uncertainty in expert and decision support systems is an area of c

9、ontinual debate. In this aspect, fuzzy logic provides a better, more consistent, and more mathematically sound method of handling uncertainties. .,VII. Nave Thoughts on Fuzzy,Fuzzy phenomena and fuzzy concepts e.g. “rain” is a nature phenomenon. mizzle downpour,Fuzzy partition: light rain，moderate r

10、ain，heavy rain 比如，解釋“大雨”，專業(yè)的天氣預(yù)報(bào)書籍可能解釋為“二十四小時(shí)內(nèi)雨量累計(jì)(在雨量收集器內(nèi))達(dá)40至79.9毫米（mm）雨”，這是十分精確的。 Fuzzy judgment: What kind of rain is it now？ Fuzzy inference: predicting a good, fair, or poor harvest this year based on the results of fuzzy judging.,e.g.1 電腦不如人腦 兩歲的小孩 圖像識(shí)別能力 語音識(shí)別能力,IQ,EQ,Science：猴子可通過思維代替“手”操作電腦

11、,e.g. 2 “請(qǐng)你十點(diǎn)左右在行政大樓附近等我一下” Where When,聽不懂?,Examples on fuzzy concepts,Consider the following statements,The engine temperature is hot.,Current inflation rates are rising rapidly.,CPI消費(fèi)者價(jià)格指數(shù) PPI生產(chǎn)者價(jià)格指數(shù),Examples on fuzzy concepts,Tom is rather tall, but Judy is short. If you are tall, than you are qu

12、ite likely heavy.,Examples on fuzzy concepts,The description of a human characteristic such as healthy. The classification of patients as depressed. The classification of certain objects as large. The classification of people by age such as old. A rule for driving such as “if an obstacle is close, t

13、hen brake immediately”.,Examples on fuzzy concepts,Examples on fuzzy concepts,Yes or No,10 years and 6 months of imprisonment,Death penalty,如果有一天我們能建立法律公式,Concept and set,intension (內(nèi)涵)：attributes of the object concept extension (外延)：all of the objects defined by the concept（set） G. Cantor (1887):,I

14、f a fuzzy concept can be rigidly described by Cantors notion of sets or the bivalent (true/false or two-valued) logic？,模糊概念能否用Cantor集合來刻畫？,禿頭悖論 一位已經(jīng)謝頂?shù)睦辖淌谂c他的學(xué)生爭(zhēng)論他是否為禿頭問題。 教授：我是禿頭嗎？ 學(xué)生：您的頭頂上已經(jīng)沒有多少頭發(fā)，確實(shí)應(yīng)該說是。 教授：你秀發(fā)稠密，絕對(duì)不算禿頭，問你，如果你頭上脫落了一根頭發(fā)之后，能說變成了禿頭了嗎？ 學(xué)生：我減少一根頭發(fā)之后，當(dāng)然不會(huì)變成禿頭。 教授：好了，總結(jié)我們的討論，得出下面的命題：如果一個(gè)人不是禿頭，那么他減少一根頭發(fā)仍不是禿頭，你說對(duì)嗎？ 學(xué)生：對(duì)！ 教授：我年輕時(shí)代也和你一樣一頭秀發(fā)，當(dāng)時(shí)沒有人說我禿頭，后來隨著年齡的增高，頭發(fā)一根根減少到今天的樣子。但每掉一根頭發(fā)，根據(jù)我們剛才的命題，我都不應(yīng)該稱為禿頭，這樣經(jīng)有限次頭發(fā)的減少，用這一命題有限次，結(jié)論是：我今天仍不是禿頭。,Postulate: If a man with n (a nature number) hairs is baldheaded, then so is a man with n+1 hairs. Baldh