模糊控制理論畢業(yè)設(shè)計(jì)(論文)外文文獻(xiàn)翻譯

1、模糊控制理論-畢業(yè)設(shè)計(jì)(論文)外文文獻(xiàn)翻譯 模糊控制理論摘自 維基百科 2011年11月20日概述 模糊邏輯廣泛適用于機(jī)械控制。這個(gè)詞本身激發(fā)一個(gè)一定的懷疑,試探相當(dāng)于“倉(cāng)促的邏輯”或“虛假的邏輯”,但“模糊”不是指一個(gè)部分缺乏嚴(yán)格性的方法,而這樣的事實(shí),即邏輯涉及能處理的概念,不能被表達(dá)為“對(duì)”或“否”,而是因?yàn)椤安糠终鎸?shí)”。雖然遺傳算法和神經(jīng)網(wǎng)絡(luò)可以執(zhí)行一樣模糊邏輯在很多情況下,模糊邏輯的優(yōu)點(diǎn)是解決這個(gè)問(wèn)題的方法,能夠被鑄造方面接線員能了解,以便他們的經(jīng)驗(yàn),可用于設(shè)計(jì)的控制器。這讓它更容易完成機(jī)械化已成功由人執(zhí)行。歷史以及應(yīng)用 模糊邏輯首先被提出是有l(wèi)otfi在加州大學(xué)伯克利分校在1965

2、年的一篇論文。他闡述了他的觀點(diǎn)在1973年的一篇論文的概念,介紹了語(yǔ)言變量”,在這篇文章中相當(dāng)于一個(gè)變量定義為一個(gè)模糊集合。其他研究打亂了,第二次工業(yè)應(yīng)用中,水泥窯建在丹麥,即將到來(lái)的在線1975。 模糊系統(tǒng)在很大程度上在美國(guó)被忽略了,因?yàn)樗麄兏嚓P(guān)注的是人工智能,一個(gè)被過(guò)分吹噓的領(lǐng)域,尤其是在1980年中期年代,導(dǎo)致在誠(chéng)信缺失的商業(yè)領(lǐng)域。 然而日本人對(duì)這個(gè)卻沒(méi)有偏見(jiàn)和忽略,模糊系統(tǒng)引發(fā)日立的seiji yasunobu和soji yasunobu miyamoto的興趣。,他于1985年的模擬,證明了模糊控制系統(tǒng)對(duì)仙臺(tái)鐵路的控制的優(yōu)越性。他們的想法是被接受了,并將模糊系統(tǒng)用來(lái)控制加速、制動(dòng)、

3、和停車,當(dāng)線于1987年開(kāi)業(yè)。 1987年另一項(xiàng)促進(jìn)模糊系統(tǒng)的興趣。在一個(gè)國(guó)際會(huì)議在東京的模糊研究那一年,yamakawa論證使用模糊控制,通過(guò)一系列簡(jiǎn)單的專用模糊邏輯芯片,在一個(gè)“倒立擺“實(shí)驗(yàn)。這是一個(gè)經(jīng)典的控制問(wèn)題,在這一過(guò)程中,車輛努力保持桿安裝在頂部用鉸鏈正直來(lái)回移動(dòng)。 這次展示給觀察者家們留下了深刻的印象,以及后來(lái)的實(shí)驗(yàn),他登上一yamakawa酒杯包含水或甚至一只活老鼠的頂部的鐘擺。該系統(tǒng)在兩種情況下,保持穩(wěn)定。yamakawa最終繼續(xù)組織自己的fuzzy-systems研究實(shí)驗(yàn)室?guī)椭米约旱膶＠谔锏乩锏臅r(shí)候。 展示之后,日本工程師開(kāi)發(fā)出了大范圍的模糊系統(tǒng)用于工業(yè)領(lǐng)域和消費(fèi)領(lǐng)域

4、的應(yīng)用。1988年,日本建立了國(guó)際模糊工程實(shí)驗(yàn)室,建立合作安排48公司進(jìn)行模糊控制的研究。 松下吸塵器使用微控制器運(yùn)行模糊算法去控制傳感器和調(diào)整吸塵力。日立洗衣機(jī)用模糊控制器load-weight,fabric-mix和塵土傳感器及自動(dòng)設(shè)定洗滌周期來(lái)最佳利用電能、水和洗滌劑。 佳能研制出的一種上相機(jī)使用電荷耦合器件ccd測(cè)量中的圖像清晰的六個(gè)區(qū)域其視野和使用提供的信息來(lái)決定是否這個(gè)影像在焦點(diǎn)上清晰。它也可以追蹤變化的速率在鏡頭運(yùn)動(dòng)的重點(diǎn),以及它的速度以防止控制超調(diào)。相機(jī)的模糊控制系統(tǒng)采用12輸入,6個(gè)輸入了解解現(xiàn)行清晰所提供的數(shù)據(jù)和其他6個(gè)輸入測(cè)量ccd鏡頭的變化率的運(yùn)動(dòng)。輸出的位置是鏡頭。模

5、糊控制系統(tǒng)應(yīng)用13條規(guī)則,需要1.1 千字節(jié)記憶信息。 另外一個(gè)例子是,三菱工業(yè)空調(diào)設(shè)計(jì)采用25加熱規(guī)則和25冷卻規(guī)則。溫度傳感器提供輸入,輸出一個(gè)控制逆變器,一個(gè)壓縮機(jī)氣閥,風(fēng)扇電機(jī)。和以前的設(shè)計(jì)相比,新設(shè)計(jì)的模糊控制器增加五次加熱冷卻速度,降低能耗24%,增加溫度穩(wěn)定性的一個(gè)因素兩個(gè),使用較少的傳感器。 日本人對(duì)模糊邏輯的人情是反映在很廣泛的應(yīng)用范圍上,他們一直在研究或?qū)崿F(xiàn):例如個(gè)性和筆跡識(shí)別光學(xué)模糊系統(tǒng),機(jī)器人,聲控機(jī)器人直升飛機(jī)。 模糊系統(tǒng)的相關(guān)研究工作也在美國(guó)和歐洲進(jìn)行著。美國(guó)環(huán)境保護(hù)署分析了模糊控制節(jié)能電動(dòng)機(jī),美國(guó)國(guó)家航空和宇宙航行局研究了模糊控制自動(dòng)太空對(duì)接。仿真結(jié)果表明,模糊控

6、制系統(tǒng)可大大降低燃料消耗。如波音公司、通用汽車、艾倫-布拉德利、克萊斯勒、伊頓,和漩渦了模糊邏輯用于低功率冰箱、改善汽車變速箱。在1995年美泰克公司推出的一個(gè)“聰明” 基于模糊控制器洗碗機(jī),“一站式感應(yīng)模塊”包括熱敏電阻器,用來(lái)溫度測(cè)量;電導(dǎo)率傳感器,用來(lái)測(cè)量離子洗滌劑水平存在于洗;分散和濁度傳感器用來(lái)檢測(cè)透射光測(cè)量失禁的洗滌,以及一個(gè)磁致伸縮傳感器來(lái)讀取旋轉(zhuǎn)速率。這個(gè)系統(tǒng)確定最優(yōu)洗周期任何載荷,獲得最佳的結(jié)果用最少的能源、洗滌劑、和水。 研究和開(kāi)發(fā)還繼續(xù)模糊應(yīng)用軟件,作為反對(duì)固件設(shè)計(jì),包括模糊專家系統(tǒng)模糊邏輯與整合神經(jīng)網(wǎng)絡(luò)和所謂的自適應(yīng)遺傳軟件系統(tǒng),其最終目的是建立“自主學(xué)習(xí)”模糊控制系統(tǒng)

7、。模糊集 輸入變量在一個(gè)模糊控制系統(tǒng)是集映射到一般由類似的隸屬度函數(shù),稱為“模糊集”。轉(zhuǎn)換的過(guò)程中,一個(gè)干脆利落的輸入值模糊值稱為“模糊化”。 一個(gè)控制系統(tǒng)也有各種不同的類型開(kāi)關(guān)或“開(kāi)關(guān)”,連同它的模擬輸入輸入,而這樣的開(kāi)關(guān)輸入當(dāng)然總有一個(gè)真實(shí)的價(jià)值等于要么1或0,但該方案能對(duì)付他們,簡(jiǎn)單的模糊函數(shù),要么發(fā)生一個(gè)值或另一個(gè)。 賦予了“映射輸入變量的隸屬函數(shù)和進(jìn)入真理價(jià)值,單片機(jī)然后做出決定為采取何種行動(dòng)基于一套“規(guī)則”,每一組的形式。 在一個(gè)例子里,有兩個(gè)輸入變量是“剎車溫度”和“速度”,定義為模糊集值。輸出變量,“制動(dòng)壓力” ,也定義為一個(gè)模糊集,有價(jià)值觀像“靜” 、“稍微增大” “略微下降

8、”,等等。這條規(guī)則本身很莫名其妙,因?yàn)樗雌饋?lái)好像可以使用,會(huì)干擾到與模糊,但要記住,這個(gè)決定是基于一套規(guī)則。 所有的規(guī)則都調(diào)用申請(qǐng),使用模糊隸屬度函數(shù)和誠(chéng)實(shí)得到輸入值,確定結(jié)果的規(guī)則。這個(gè)結(jié)果將被映射成一個(gè)隸屬函數(shù)和控制輸出變量的真值。這些結(jié)果相結(jié)合,給出了具體的“脆”的答案,實(shí)際的制動(dòng)壓力,一個(gè)過(guò)程被稱為解模糊化,結(jié)合了模糊操作規(guī)則 推理“描述”模糊專家系統(tǒng)”。 傳統(tǒng)的控制系統(tǒng)是基于數(shù)學(xué)模型的控制系統(tǒng),描述了使用一個(gè)或更多微分方程確定系統(tǒng)回應(yīng)其輸入。這類系統(tǒng)通常被作為“pid控制器”他們是產(chǎn)品的數(shù)十年的發(fā)展建設(shè)和理論分析,是非常有效的。 如果pid和其他傳統(tǒng)的控制系統(tǒng)是如此的先進(jìn),何必還要

9、模糊控制嗎?它有一些優(yōu)點(diǎn)。在許多情況下,數(shù)學(xué)模型的控制過(guò)程可能不存在,或太“貴”的認(rèn)識(shí)論的計(jì)算機(jī)處理能力和內(nèi)存,與系統(tǒng)的基于經(jīng)驗(yàn)規(guī)則可能更有效。 此外,模糊邏輯都適合低成本實(shí)現(xiàn)基于廉價(jià)的傳感器、低分辨率模擬/數(shù)字轉(zhuǎn)換器,或8位單片機(jī)芯片one-chip 4比特。這種系統(tǒng)可以很容易地通過(guò)增加新的規(guī)則升級(jí)來(lái)提高性能或添加新功能。在許多情況下,模糊控制可以用來(lái)改善現(xiàn)有的傳統(tǒng)控制器系統(tǒng)通過(guò)增加了額外的情報(bào)電流控制方法。模糊控的細(xì)節(jié) 模糊控制器是很簡(jiǎn)單的理念上。它們是由一個(gè)輸入階段,一個(gè)處理階段,一個(gè)輸出階段。地圖傳感器輸入級(jí)或其他輸入,比如開(kāi)關(guān)等等,到合適的隸屬函數(shù)和真理的價(jià)值。每一個(gè)適當(dāng)?shù)募庸るA段調(diào)

10、用規(guī)則和產(chǎn)生的結(jié)果對(duì)每個(gè)人來(lái)說(shuō),然后結(jié)合結(jié)果的規(guī)則。最后,將結(jié)果輸出階段相結(jié)合的具體控制輸出回他的價(jià)值。 最常見(jiàn)的形狀是三角形的隸屬度函數(shù),盡管梯形和貝爾曲線也使用,但其形狀通常比數(shù)量更重要曲線及其位置。從三人至七人通常是適當(dāng)?shù)母采w曲線所需要的范圍的一個(gè)輸入值,或“宇宙的話語(yǔ)“在模糊術(shù)語(yǔ)。 作為討論之前,加工階段是基于規(guī)則的集合的形式邏輯if - then報(bào)表,那里的部分叫做“之前”和后來(lái)的部分被稱為“隨之”。典型的模糊控制系統(tǒng)具有幾十個(gè)規(guī)則。 這條規(guī)則的價(jià)值采用真理“溫”的輸入,真值的“冷”,產(chǎn)生的結(jié)果,在模糊集的“加熱器“輸出,“高”的價(jià)值。這個(gè)結(jié)果是用來(lái)與其他規(guī)則的結(jié)果,最終產(chǎn)生脆復(fù)合輸

11、出。很明顯,越是真理價(jià)值的“冷”,真值越高,“高”,但這并不一定就意味著輸出本身會(huì)被設(shè)置為“高”,因?yàn)檫@是唯一準(zhǔn)則在許多。在某些情況下,隸屬函數(shù)可以修正“籬笆”相當(dāng)于形容詞。模糊限制語(yǔ)包括“關(guān)于“常見(jiàn),“近”、“接近”、“大約”、“很”、“稍微”、“太”、“非?！?、“有點(diǎn)”。這些操作可能有明確的定義,雖然可能有很大差別的定義不同的實(shí)現(xiàn)?！胺浅！?因?yàn)橐粋€(gè)典型的例子,廣場(chǎng)隸屬函數(shù);因?yàn)闀?huì)員價(jià)值總是小于1,這減少了隸屬函數(shù)?！胺浅！绷⒎襟w價(jià)值觀提供更大的縮小,而“有點(diǎn)“擴(kuò)大功能以平方根的計(jì)算。 在實(shí)踐中,模糊規(guī)則集,通常有幾個(gè)來(lái)路綜合利用模糊運(yùn)算,如,或者,不,雖然再次定義每每變化,在一個(gè)受歡迎的

12、定義,只是利用最小重量的雛形,而或采用最大值。還有一個(gè)不經(jīng)營(yíng)者一個(gè)隸屬函數(shù)減去從1到給“補(bǔ)充性”功能。 有幾種方法可以定義一個(gè)規(guī)則的結(jié)果,而是一種最常見(jiàn)的和最簡(jiǎn)單的是“極大極小“推理法,給出了輸出隸屬函數(shù)的真值所產(chǎn)生的前提。 規(guī)則可以解決并聯(lián)在硬件或軟件。順序結(jié)果所有的規(guī)則,其中的幾個(gè)方法。在理論上有幾十個(gè),每個(gè)都有各種各樣的優(yōu)點(diǎn)和缺點(diǎn)。 “質(zhì)心”的方法很受歡迎,在“的質(zhì)心”的結(jié)果提供了清新的價(jià)值。另一個(gè)方法是“高度”方法,它以價(jià)值的主要因素。方法更利于統(tǒng)治質(zhì)心與輸出最大的區(qū)域,而高程法顯然更利于規(guī)則和最大的輸出值。 模糊控制系統(tǒng)的設(shè)計(jì)是基于經(jīng)驗(yàn)方法,基本上一個(gè)系統(tǒng)的方法試誤。大致過(guò)程如下:

13、1.文件系統(tǒng)的操作規(guī)范和輸入與輸出。 2.文檔模糊集的輸入。 3.文件規(guī)則集。 4.確定解模糊化方法確定。 5.運(yùn)行測(cè)試套件驗(yàn)證通過(guò)制度,調(diào)整細(xì)節(jié)的要求。 6.完整的文件,發(fā)布給生產(chǎn)。邏輯解釋模糊控制 盡管有幾個(gè)困難出現(xiàn)給一個(gè)嚴(yán)謹(jǐn)?shù)倪壿嫿忉宨f - then規(guī)則。作為一個(gè)例子,解釋一個(gè)規(guī)則,因?yàn)槿绻麥囟仁恰袄洹?那么加熱器是“高”由第一階表達(dá)式冷高和假設(shè)是一個(gè)輸入這樣冷是假的。然后公式冷高是適用于任何一個(gè)師,因此任何不正確的控制提供了一種給r。很明顯,如果我們考慮系統(tǒng)的先例的規(guī)則類定義一個(gè)分區(qū)這樣一個(gè)自相矛盾的現(xiàn)象不會(huì)出現(xiàn)。在任何情況下它有時(shí)是不考慮兩個(gè)變量和在一條規(guī)則沒(méi)有某種功能的依賴。嚴(yán)謹(jǐn)

14、的邏輯正當(dāng)化中給出的模糊控制hajek的書,被描繪成一個(gè)模糊控制理論的基本hajek邏輯。在2005 gerla模糊控制邏輯方法,提出了一種基于以下的想法。f模糊函數(shù)表示的系統(tǒng)與模糊控制相結(jié)合,即:給定輸入,是模糊集合可能的輸出。然后給出一個(gè)可能的輸出的,我們把為真理程度的表示。更多的是任何系統(tǒng)的if - then規(guī)則可轉(zhuǎn)化為一個(gè)模糊的程序,在這種情況下模糊函數(shù)模糊謂詞的解釋很好在相關(guān)的最小模糊herbrand模型。以這樣一種方式成為一個(gè)章模糊控制的模糊邏輯編程。學(xué)習(xí)過(guò)程成為一個(gè)問(wèn)題屬于歸納邏輯理論。fuzzy controlfrom wikipedia20 november 2011over

15、view fuzzy logic is widely used in machine control. the term itself inspires a certain skepticism, sounding equivalent to half-baked logic or bogus logic, but the fuzzy part does not refer to a lack of rigour in the method, rather to the fact that the logic involved can deal with concepts that canno

16、t be expressed as true or false but rather as partially true. although genetic algorithms and neural networks can perform just as well as fuzzy logic in many cases, fuzzy logic has the advantage that the solution to the problem can be cast in terms that human operators can understand, so that their

17、experience can be used in the design of the controller. this makes it easier to mechanize tasks that are already successfully performed by humanshistory and applications fuzzy logic was first proposed by lotfi a. zadeh of the university of california at berkeley in a 1965 paper. he elaborated on his

18、 ideas in a 1973 paper that introduced the concept of linguistic variables, which in this article equates to a variable defined as a fuzzy set. other research followed, with the first industrial application, a cement kiln built in denmark, coming on line in 1975fuzzy systems were largely ignored in

19、the u.s. because they were associated with artificial intelligence, a field that periodically oversells itself, especially in the mid-1980s, resulting in a lack of credibility within the commercial domainthe japanese did not have this prejudice. interest in fuzzy systems was sparked by seiji yasunob

20、u and soji miyamoto of hitachi, who in 1985 provided simulations that demonstrated the superiority of fuzzy control systems for the sendai railway. their ideas were adopted, and fuzzy systems were used to control accelerating, braking, and stopping when the line opened in 1987another event in 1987 h

21、elped promote interest in fuzzy systems. during an international meeting of fuzzy researchers in tokyo that year, takeshi yamakawa demonstrated the use of fuzzy control, through a set of simple dedicated fuzzy logic chips, in an inverted pendulum experiment. this is a classic control problem, in whi

22、ch a vehicle tries to keep a pole mounted on its top by a hinge upright by moving back and forthobservers were impressed with this demonstration, as well as later experiments by yamakawa in which he mounted a wine glass containing water or even a live mouse to the top of the pendulum. the system mai

23、ntained stability in both cases. yamakawa eventually went on to organize his own fuzzy-systems research lab to help exploit his patents in the fieldfollowing such demonstrations, japanese engineers developed a wide range of fuzzy systems for both industrial and consumer applications. in 1988 japan e

24、stablished the laboratory for international fuzzy engineering life, a cooperative arrangement between 48 companies to pursue fuzzy researchmatsushita vacuum cleaners use micro controllers running fuzzy algorithms to interrogate dust sensors and adjust suction power accordingly. hitachi washing machi

25、nes use fuzzy controllers to load-weight, fabric-mix, and dirt sensors and automatically set the wash cycle for the best use of power, water, and detergentcanon developed an autofocusing camera that uses a charge-coupled device ccd to measure the clarity of the image in six regions of its field of v

26、iew and use the information provided to determine if the image is in focus. it also tracks the rate of change of lens movement during focusing, and controls its speed to prevent overshoot.the cameras fuzzy control system uses 12 inputs: 6 to obtain the current clarity data provided by the ccd and 6

27、to measure the rate of change of lens movement. the output is the position of the lens. the fuzzy control system uses 13 rules and requires 1.1 kilobytes of memoryas another example of a practical system, an industrial air conditioner designed by mitsubishi uses 25 heating rules and 25 cooling rules

28、. a temperature sensor provides input, with control outputs fed to an inverter, a compressor valve, and a fan motor. compared to the previous design, the fuzzy controller heats and cools five times faster, reduces power consumption by 24%, increases temperature stability by a factor of two, and uses

29、 fewer sensors. the enthusiasm of the japanese for fuzzy logic is reflected in the wide range of other applications they have investigated or implemented: character and handwriting recognition; optical fuzzy systems; robots, voice-controlled robot helicopters work on fuzzy systems is also proceeding

30、 in the us and europe. the us environmental protection agency has investigated fuzzy control for energy-efficient motors, and nasa has studied fuzzy control for automated space docking: simulations show that a fuzzy control system can greatly reduce fuel consumption. firms such as boeing, general mo

31、tors, allen-bradley, chrysler, eaton, and whirlpool have worked on fuzzy logic for use in low-power refrigerators, improved automotive transmissions, and energy-efficient electric motors. in 1995 maytag introduced an intelligent dishwasher based on a fuzzy controller and a one-stop sensing module th

32、at combines a thermistor, for temperature measurement; a conductivity sensor, to measure detergent level from the ions present in the wash; a turbidity sensor that measures scattered and transmitted light to measure the soiling of the wash; and a magnetostrictive sensor to read spin rate. the system

33、 determines the optimum wash cycle for any load to obtain the best results with the least amount of energy, detergent, and water research and development is also continuing on fuzzy applications in software, as opposed to firmware, design, including fuzzy expert systems and integration of fuzzy logi

34、c with neural-network and so-called adaptive genetic software systems, with the ultimate goal of building self-learning fuzzy control systems.fuzzy sets the input variables in a fuzzy control system are in general mapped into by sets of membership functions similar to this, known as fuzzy sets. the

35、process of converting a crisp input value to a fuzzy value is called fuzzification.a control system may also have various types of switch, or on-off, inputs along with its analog inputs, and such switch inputs of course will always have a truth value equal to either 1 or 0, but the scheme can deal w

36、ith them as simplified fuzzy functions that happen to be either one value or anothergiven mappings of input variables into membership functions and truth values, the microcontroller then makes decisions for what action to take based on a set of rules, each of the formin one example, the two input va

37、riables are brake temperature and speed that have values defined as fuzzy sets. the output variable, brake pressure, is also defined by a fuzzy set that can have values like static, slightly increased, slightly decreased, and so on.this rule by itself is very puzzling since it looks like it could be

38、 used without bothering with fuzzy logic, but remember that the decision is based on a set of rules: all the rules that apply are invoked, using the membership functions and truth values obtained from the inputs, to determine the result of the rulethis result in turn will be mapped into a membership

39、 function and truth value controlling the output variablethese results are combined to give a specific crisp answer, the actual brake pressure, a procedure known as defuzzification.this combination of fuzzy operations and rule-based inference describes a fuzzy expert systemtraditional control system

40、s are based on mathematical models in which the control system is described using one or more differential equations that define the system response to its inputs. such systems are often implemented as pid controllers proportional-integral-derivative controllers. they are the products of decades of

41、development and theoretical analysis, and are highly effectiveif pid and other traditional control systems are so well-developed, why bother with fuzzy control? it has some advantages. in many cases, the mathematical model of the control process may not exist, or may be too expensive in terms of com

42、puter processing power and memory, and a system based on empirical rules may be more effective.furthermore, fuzzy logic is well suited to low-cost implementations based on cheap sensors, low-resolution analog-to-digital converters, and 4-bit or 8-bit one-chip microcontroller chips. such systems can

43、be easily upgraded by adding new rules to improve performance or add new features. in many cases, fuzzy control can be used to improve existing traditional controller systems by adding an extra layer of intelligence to the current control method.fuzzy control in detail fuzzy controllers are very sim

44、ple conceptually. they consist of an input stage, a processing stage, and an output stage. the input stage maps sensor or other inputs, such as switches, thumbwheels, and so on, to the appropriate membership functions and truth values. the processing stage invokes each appropriate rule and generates

45、 a result for each, then combines the results of the rules. finally, the output stage converts the combined result back into a specific control output valuethe most common shape of membership functions is triangular, although trapezoidal and bell curves are also used, but the shape is generally less

46、 important than the number of curves and their placement. from three to seven curves are generally appropriate to cover the required range of an input value, or the universe of discourse in fuzzy jargonas discussed earlier, the processing stage is based on a collection of logic rules in the form of

47、if-then statements, where the if part is called the antecedent and the then part is called the consequent this rule uses the truth value of the temperature input, which is some truth value of cold, to generate a result in the fuzzy set for the heater output, which is some value of high. this result

48、is used with the results of other rules to finally generate the crisp composite output. obviously, the greater the truth value of cold, the higher the truth value of high, though this does not necessarily mean that the output itself will be set to high since this is only one rule among many. in some

49、 cases, the membership functions can be modified by hedges that are equivalent to adjectives. common hedges include about, near, close to, approximately, very, slightly, too, extremely, and somewhat. these operations may have precise definitions, though the definitions can vary considerably between

50、different implementations. very, for one example, squares membership functions; since the membership values are always less than 1, this narrows the membership function. extremely cubes the values to give greater narrowing, while somewhat broadens the function by taking the square rootin practice, t

51、he fuzzy rule sets usually have several antecedents that are combined using fuzzy operators, such as and, or, and not, though again the definitions tend to vary: and, in one popular definition, simply uses the minimum weight of all the antecedents, while or uses the imum value. there is also a not o

52、perator that subtracts a membership function from 1 to give the complementary functionthere are several ways to define the result of a rule, but one of the most common and simplest is the -min inference method, in which the output membership function is given the truth value generated by the premise

53、rules can be solved in parallel in hardware, or sequentially in software. the results of all the rules that have fired are defuzzified to a crisp value by one of several methods. there are dozens in theory, each with various advantages and drawbacksthe centroid method is very popular, in which the center of mass of the result provides the crisp value. another approach is the height method, which takes the