第一篇：畢業(yè)設計(論文)外文文獻翻譯要求及封面

畢業(yè)設計（論文）外文文獻翻譯要求

根據(jù)《普通高等學校本科畢業(yè)設計（論文）指導》的內(nèi)容，特對外文文獻翻譯提出以下要求：

一、翻譯的外文文獻一般為1～2篇，外文字符要求不少于1.5萬（或翻譯成中文后至少在3000字以上）。

二、翻譯的外文文獻應主要選自學術期刊、學術會議的文章、有關著作及其他相關材料，應與畢業(yè)論文（設計）主題相關，并作為外文參考文獻列入畢業(yè)論文（設計）的參考文獻。并在每篇中文譯文首頁用“腳注”形式注明原文作者及出處，中文譯文后應附外文原文。

三、中文譯文的基本撰寫格式為題目采用小三號黑體字居中打印，正文采用宋體小四號字，行間距一般為固定值20磅，標準字符間距。頁邊距為左3cm，右2.5cm，上下各2.5cm，頁面統(tǒng)一采用A4紙。

四、封面格式由學校統(tǒng)一制作（注：封面上的“翻譯題目”指中文譯文的題目，附件1為一篇外文翻譯的封面格式，附件二為兩篇外文翻譯的封面格式），若有兩篇外文文獻，請按“封面、譯文

一、外文原文

一、譯文

二、外文原文二”的順序統(tǒng)一裝訂。

教務處

2006年2月27日

杭州電子科技大學

畢業(yè)設計（論文）外文文獻翻譯

畢業(yè)設計（論文）題目

翻譯題目

學院

專業(yè)

姓名

班級

學號

指導教師

杭州電子科技大學

畢業(yè)設計（論文）外文文獻翻譯

畢業(yè)設計（論文）題目

翻譯（1）題目 翻譯（2）題目

學院

專業(yè)

姓名

班級

學號

指導教師

第二篇：畢業(yè)設計(論文)外文文獻翻譯要求

畢業(yè)設計（論文）外文文獻翻譯要求

根據(jù)《浙江省教育廳高教處關于對高等學校2004屆本?？茖W生畢業(yè)設計（論文）進行抽查的通知》的評審要求，“本科畢業(yè)論文要求翻譯外文文獻2篇以上”。為提高畢業(yè)論文（設計）的質(zhì)量，并與教育廳評審要求相一致，經(jīng)研究決定，2005屆畢業(yè)論文（設計）要求翻譯2篇外文文獻，外文字符不少于1.5萬, 每篇外文文獻翻譯的中文字數(shù)一般要求2000－3000左右。

翻譯的外文文獻應主要選自學術期刊、學術會議的文章、有關著作及其他相關材料，應與畢業(yè)論文（設計）主題相關，并作為外文參考文獻列入畢業(yè)論文（設計）的參考文獻。并在每篇中文譯文首頁用“腳注”形式注明原文作者及出處，中文譯文后應附外文原文。中文譯文的基本撰寫格式為題目采用小三號黑體字居中打印，正文采用宋體五號字，行間距一般為固定值20磅，標準字符間距。

湖州師范學院（求真學院）

畢業(yè)設計（論文）外文文獻翻譯

畢業(yè)設計（論文）題目

翻譯（1）題目

翻譯（2）題目

學院 專業(yè) 姓名 班級 學號 指導教師

第三篇：4畢業(yè)設計(論文)外文文獻翻譯范文

黃石理工學院畢業(yè)設計（論文）外文文獻翻譯

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械控制。這個詞本身激發(fā)一個一定的懷疑,試探相當于“倉促的邏輯”或“虛假的邏輯”,但“模糊”不是指一個部分缺乏嚴格性的方法,而這樣的事實,即邏輯涉及能處理的概念,不能被表達為“對”或“否”,而是因為“部分真實”。雖然遺傳算法和神經(jīng)網(wǎng)絡可以執(zhí)行一樣模糊邏輯在很多情況下,模糊邏輯的優(yōu)點是解決這個問題的方法,能夠被鑄造方面接線員能了解,以便他們的經(jīng)驗,可用于設計的控制器。這讓它更容易完成機械化已成功由人執(zhí)行。

歷史以及應用

模糊邏輯首先被提出是有Lotfi在加州大學伯克利分校在1965年的一篇論文。他闡述了他的觀點在1973年的一篇論文的概念,介紹了語言變量”,在這篇文章中相當于一個變量定義為一個模糊集合。其他研究打亂了,第二次工業(yè)應用中,水泥窯建在丹麥,即將到來的在線1975。

模糊系統(tǒng)在很大程度上在美國被忽略了,因為他們更多關注的是人工智能，一個被過分吹噓的領域，尤其是在1980年中期年代,導致在誠信缺失的商業(yè)領域。

然而日本人對這個卻沒有偏見和忽略，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)對仙臺鐵路的控制的優(yōu)越性。他們的想法是被接受了,并將模糊系統(tǒng)用來控制加速、制動、和停車，當線于1987年開業(yè)。

1987年另一項促進模糊系統(tǒng)的興趣。在一個國際會議在東京的模糊研究那一年,Yamakawa論證<使用模糊控制,通過一系列簡單的專用模糊邏輯芯片,在一個“倒立擺“實驗。這是一個經(jīng)典的控制問題,在這一過程中,車輛努力保持桿安裝在頂部用鉸鏈正直來回移動。

這次展示給觀察者家們留下了深刻的印象,以及后來的實驗,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研究實驗室?guī)椭米约旱膶＠谔锏乩锏臅r候。

黃石理工學院畢業(yè)設計（論文）外文文獻翻譯

展示之后,日本工程師開發(fā)出了大范圍的模糊系統(tǒng)用于工業(yè)領域和消費領域的應用。1988年,日本建立了國際模糊工程實驗室,建立合作安排48公司進行模糊控制的研究。

松下吸塵器使用微控制器運行模糊算法去控制傳感器和調(diào)整吸塵力。日立洗衣機用模糊控制器Load-Weight,Fabric-Mix和塵土傳感器及自動設定洗滌周期來最佳利用電能、水和洗滌劑。

佳能研制出的一種上相機使用電荷耦合器件(CCD)測量中的圖像清晰的六個區(qū)域其視野和使用提供的信息來決定是否這個影像在焦點上(清晰)。它也可以追蹤變化的速率在鏡頭運動的重點,以及它的速度以防止控制超調(diào)。相機的模糊控制系統(tǒng)采用12輸入,6個輸入了解解現(xiàn)行清晰所提供的數(shù)據(jù)和其他6個輸入測量CCD鏡頭的變化率的運動。輸出的位置是鏡頭。模糊控制系統(tǒng)應用13條規(guī)則,需要1.1 千字節(jié)記憶信息。

另外一個例子是,三菱工業(yè)空調(diào)設計采用25加熱規(guī)則和25冷卻規(guī)則。溫度傳感器提供輸入,輸出一個控制逆變器,一個壓縮機氣閥,風扇電機。和以前的設計相比,新設計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)定性的一個因素兩個,使用較少的傳感器。

日本人對模糊邏輯的人情是反映在很廣泛的應用范圍上,他們一直在研究或?qū)崿F(xiàn):例如個性和筆跡識別光學模糊系統(tǒng),機器人,聲控機器人直升飛機。

模糊系統(tǒng)的相關研究工作也在美國和歐洲進行著。美國環(huán)境保護署分析了模糊控制節(jié)能電動機,美國國家航空和宇宙航行局研究了模糊控制自動太空對接。仿真結(jié)果表明,模糊控制系統(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“聰明” 基于模糊控制器洗碗機，“一站式感應模塊”包括熱敏電阻器,用來溫度測量;電導率傳感器,用來測量離子洗滌劑水平存在于洗;分散和濁度傳感器用來檢測透射光測量失禁的洗滌,以及一個磁致伸縮傳感器來讀取旋轉(zhuǎn)速率。這個系統(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。

研究和開發(fā)還繼續(xù)模糊應用軟件,作為反對固件設計,包括模糊專家系統(tǒng)模糊邏輯與整合神經(jīng)網(wǎng)絡和所謂的自適應遺傳軟件系統(tǒng),其最終目的是建立“自主學習”模糊控制系統(tǒng)。

黃石理工學院畢業(yè)設計（論文）外文文獻翻譯

模糊集

輸入變量在一個模糊控制系統(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)換的過程中,一個干脆利落的輸入值模糊值稱為“模糊化”。

一個控制系統(tǒng)也有各種不同的類型開關或“開關”,連同它的模擬輸入輸入,而這樣的開關輸入當然總有一個真實的價值等于要么1或0,但該方案能對付他們,簡單的模糊函數(shù),要么發(fā)生一個值或另一個。

賦予了“映射輸入變量的隸屬函數(shù)和進入真理價值,單片機然后做出決定為采取何種行動基于一套“規(guī)則”,每一組的形式。

在一個例子里,有兩個輸入變量是“剎車溫度”和“速度”,定義為模糊集值。輸出變量,“制動壓力” ,也定義為一個模糊集,有價值觀像“靜”、“稍微增大” “略微下降”,等等。

這條規(guī)則本身很莫名其妙,因為它看起來好像可以使用，會干擾到與模糊,但要記住,這個決定是基于一套規(guī)則。

所有的規(guī)則都調(diào)用申請,使用模糊隸屬度函數(shù)和誠實得到輸入值,確定結(jié)果的規(guī)則。這個結(jié)果將被映射成一個隸屬函數(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,實際的制動壓力,一個過程被稱為解模糊化，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)學模型的控制系統(tǒng),描述了使用一個或更多微分方程確定系統(tǒng)回應其輸入。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,何必還要模糊控制嗎?它有一些優(yōu)點。在許多情況下,數(shù)學模型的控制過程可能不存在,或太“貴”的認識論的計算機處理能力和內(nèi)存,與系統(tǒng)的基于經(jīng)驗規(guī)則可能更有效。

此外,模糊邏輯都適合低成本實現(xiàn)基于廉價的傳感器、低分辨率模擬/數(shù)字轉(zhuǎn)換器,或8位單片機芯片one-chip 4比特。這種系統(tǒng)可以很容易地通過增加新的規(guī)則升級來提高性能或添加新功能。在許多情況下,模糊控制可以用來改善現(xiàn)有的傳統(tǒng)控制器系統(tǒng)通過增加了額外的情報電流控制方法。

模糊控的細節(jié)

模糊控制器是很簡單的理念上。它們是由一個輸入階段,一個處理階段,一個輸

黃石理工學院畢業(yè)設計（論文）外文文獻翻譯

出階段。地圖傳感器輸入級或其他輸入,比如開關等等,到合適的隸屬函數(shù)和真理的價值。每一個適當?shù)募庸るA段調(diào)用規(guī)則和產(chǎn)生的結(jié)果對每個人來說,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值。

最常見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?shù)母采w曲線所需要的范圍的一個輸入值,或“宇宙的話語“在模糊術語。

作為討論之前,加工階段是基于規(guī)則的集合的形式邏輯IFThen規(guī)則。作為一個例子,解釋一個規(guī)則,因為如果(溫度是“冷”),那么(加熱器是“高”)由第一階表達式冷(x)→高(y)和假設r是一個輸入這樣冷(r)是假的。然后公式冷(r)→高(t)是適用于任何一個師,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)則類定義一個分區(qū)這樣一個自相矛盾的現(xiàn)象不會出現(xiàn)。在任何情況下它有時是不考慮兩個變量x和y在一條規(guī)則沒有某種功能的依賴。嚴謹?shù)倪壿嬚敾薪o出的模糊控制Hajek的書,被描繪成一個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r,s(y)?f(r,y)是模糊集合可能的輸出。然后給出一個可能的輸出的t,我們把f(r,t)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)化為一個模糊的程序,在這種情況下模糊函數(shù)f模糊謂詞的解釋很好(x,y)在相關的最小模糊Herbrand

模型。以這樣一種方式成為一個章模糊控制的模糊邏輯編程。學習過程成為一個問題屬于歸納邏輯理論。

黃石理工學院畢業(yè)設計（論文）外文文獻翻譯

Fuzzy Control From Wikipedia November 2011

Overview

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 cannot 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 experience can be used in the design of the controller.This makes it easier to mechanize tasks that are already successfully performed by humans.History 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 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 1975.Fuzzy systems were largely ignored in 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 domain.The Japanese did not have this prejudice.Interest in fuzzy systems was sparked by Seiji Yasunobu 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 1987.Another event in 1987 helped 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 which a vehicle tries to keep a pole mounted on its top by a hinge upright by moving back and forth.Observers 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 maintained stability in both cases.Yamakawa eventually went on to organize his own fuzzy-systems research lab to help exploit his patents in the field.Following such demonstrations, Japanese engineers developed a wide range of fuzzy systems for both industrial and consumer applications.In 1988 Japan established

黃石理工學院畢業(yè)設計（論文）外文文獻翻譯

the Laboratory for International Fuzzy Engineering(LIFE), a cooperative arrangement between 48 companies to pursue fuzzy research.Matsushita vacuum cleaners use micro controllers running fuzzy algorithms to interrogate dust sensors and adjust suction power accordingly.Hitachi washing machines 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 detergent.Canon 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 view 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 camera's fuzzy control system uses 12 inputs: 6 to obtain the current clarity data provided by the CCD and 6 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 memory.As another example of a practical system, an industrial air conditioner designed by Mitsubishi uses 25 heating rules and 25 cooling rules.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 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 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 Motors, 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“ that 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 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 logic with neural-network and so-called adaptive ”genetic“ software systems, with the ultimate goal of building ”self-learning“ fuzzy control systems.黃石理工學院畢業(yè)設計（論文）外文文獻翻譯

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 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 ”O(jiān)N-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 with them as simplified fuzzy functions that happen to be either one value or another.Given ”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 form.In one example, the two input variables 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 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 rule.This result in turn will be mapped into a membership function and truth value controlling the output variable.These 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 system“.Traditional control systems 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 development and theoretical analysis, and are highly effective.If 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 computer 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 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.黃石理工學院畢業(yè)設計（論文）外文文獻翻譯

Fuzzy control in detail

Fuzzy controllers are very simple 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 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 value.The most common shape of membership functions is triangular, although trapezoidal and bell curves are also used, but the shape is generally less 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 jargon.As discussed earlier, the processing stage is based on a collection of logic rules in the form of 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 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 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 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 root.In practice, the 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 maximum value.There is also a NOT operator that subtracts a membership function from 1 to give the ”complementary“ function.There are several ways to define the result of a rule, but one of the most common and simplest is the ”max-min“ inference method, in which the output membership function is given the truth value generated by the premise.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 drawbacks.The ”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 value of the biggest contributor.The centroid method favors the rule with the output of

黃石理工學院畢業(yè)設計（論文）外文文獻翻譯

greatest area, while the height method obviously favors the rule with the greatest output value.The diagram below demonstrates max-min inferring and centroid defuzzification for a system with input variables ”x“, ”y“, and ”z“ and an output variable ”n“.Note that ”mu“ is standard fuzzy-logic nomenclature for ”truth value“:

Fuzzy control system design is based on empirical methods, basically a methodical approach to trial-and-error.The general process is as follows:

1.Document the system's operational specifications and inputs and outputs.2.Document the fuzzy sets for the inputs.3.Document the rule set.4.Determine the defuzzification method.5.Run through test suite to validate system, adjust details as required.6.Complete document and release to production.Logical interpretation of fuzzy control In spite of the appearance there are several difficulties to give a rigorous logical interpretation of the IF-THEN rules.As an example, interpret a rule as IF(temperature is ”cold“)THEN(heater is ”high“)by the first order formula Cold(x)→High(y)and assume that r is an input such that Cold(r)is false.Then the formula Cold(r)→High(t)is true for any t and therefore any t gives a correct control given r.Obviously, if we consider systems of rules in which the class antecedent define a partition such a paradoxical phenomenon does not arise.In any case it is sometimes unsatisfactory to consider two variables x and y in a rule without some kind of functional dependence.A rigorous logical justification of fuzzy control is given in Hájek's book ,where fuzzy control is represented as a theory of Hájek's basic logic.Also in Gerla 2005 a logical approach to fuzzy control is proposed based on the following idea.Denote by f the fuzzy function associated with the fuzzy control system, i.e., given the input r, s(y)= f(r,y)is the fuzzy set of possible outputs.Then given a possible output 't', we interpret f(r,t)as the truth degree of the claim ”t is a good answer given r".More formally, any system of IF-THEN rules can be translate into a fuzzy program in such a way that the fuzzy function f is the interpretation of a vague predicate Good(x,y)in the associated least fuzzy Herbrand model.In such a way fuzzy control becomes a chapter of fuzzy logic programming.The learning process becomes a question belonging to inductive logic theory.

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