自走式大蒜收獲機(jī)設(shè)計,大蒜,收獲,設(shè)計 專家系統(tǒng)與應(yīng)用程序 基于模糊集理論的有效性的評估農(nóng)業(yè)機(jī)械 摘要： 農(nóng)業(yè)機(jī)械生產(chǎn)的服務(wù)質(zhì)量是代表農(nóng)業(yè)成功的基本因素之一。從這個意義上說,有一個明確需要定義這些機(jī)器質(zhì)量的具體指標(biāo),它有可能決定哪些機(jī)器適合不同工作條件。服務(wù)的技術(shù)系統(tǒng)概念的有效性代表質(zhì)量的一個綜合指標(biāo)。本文運(yùn)用模糊集理論定義的有效性和可靠性、可維護(hù)性和功能作為影響指標(biāo)的有效性。在這個意義上的模型評估的有效性拖拉機(jī)作為農(nóng)業(yè)的典型代表機(jī)器已經(jīng)形成。本模型是基于集成上述的語言描述。利用模糊集理論和max-min成分影響指標(biāo)，模型進(jìn)行了測試。同一類別的三個拖拉機(jī)為例,利用的氣候和土壤條件在更廣泛的貝爾格萊德(塞爾維亞)地區(qū)。即使在這個實(shí)驗(yàn)中條件是非常重要參數(shù) , 相比于其他操作，實(shí)現(xiàn)的效果差異也達(dá)到大致相等 。 1.介紹 為達(dá)到擴(kuò)張的全球農(nóng)產(chǎn)品的要求，實(shí)現(xiàn)更大的農(nóng)業(yè)技術(shù)的發(fā)展。人們普遍認(rèn)識到當(dāng)代農(nóng)業(yè)系統(tǒng)中需要適當(dāng)?shù)臋C(jī)器和設(shè)備，仔細(xì)和詳細(xì)規(guī)劃的需求和控制所有相關(guān)的生物、技術(shù)、技術(shù)和其他進(jìn)程。最終結(jié)果的準(zhǔn)確、可靠的預(yù)測為每個指定的操作,以及完整的作物生產(chǎn)過程中,。要求加強(qiáng)了引入復(fù)雜的實(shí)驗(yàn),數(shù)學(xué),農(nóng)業(yè)科學(xué)統(tǒng)計,機(jī)械和其他方法都是特別重要的。在過去的幾十年。除了上述的要求,一個適當(dāng)?shù)募夹g(shù)體系必須滿足生產(chǎn)力的標(biāo)準(zhǔn),期望的作物生產(chǎn)。在大多數(shù)情況下,在塞爾維亞，tractor-machinery農(nóng)場系統(tǒng)的能力遠(yuǎn)遠(yuǎn)超過最優(yōu)級別(尼克里奇′,2005),增加成本作物生產(chǎn)。目前,現(xiàn)有的數(shù)學(xué)優(yōu)化方法、支持的高性能計算機(jī)有效地解決優(yōu)化問題(Dette &韋伯達(dá)菲et al .,1990;1994;Mileusnic′,2007;等等)。一個最優(yōu)的技術(shù)體系的形成為我們生產(chǎn)了更便宜的食品,高度影響拖拉機(jī)的可靠性、可維護(hù)性和系統(tǒng)的功能。 與系統(tǒng)科學(xué)發(fā)展同樣,實(shí)際上的開始是IIWorld戰(zhàn)爭后,在適當(dāng)?shù)墓こ毯涂茖W(xué)文獻(xiàn)定義了一系列的概念,來描述技術(shù)系統(tǒng)的基本特征的點(diǎn)的服務(wù)質(zhì)量?？煽啃缘闹笜?biāo)是技術(shù)系統(tǒng)和行為操作,技術(shù)指標(biāo)和可維護(hù)性systembehaviors期間的失敗可以表示為大多數(shù)可辨認(rèn)的概念。這兩個概念及其實(shí)現(xiàn)最先進(jìn)的發(fā)展。有效性的概念被定義在試圖描述同時技術(shù)操作系統(tǒng)的行為和失敗的時期。這概念考慮可靠性和可用性的表演,以及提出了技術(shù)系統(tǒng)設(shè)計的功能(Papic&Milovanovic2007)。換句話說,一個技術(shù)系統(tǒng)的有效性的概率,一個成功的功能系統(tǒng)技術(shù)和執(zhí)行所需的準(zhǔn)則函數(shù)限制允許的差異對于給定時間和給定的周圍條件。雖然在相同的精神,一些作者定義有效性有所不同。在(Ebramhimipour &鈴木,2006)被定義為總體有效性的指標(biāo)包含效率、可靠性和可用性。這兩個引用定義包括并行關(guān)于可靠性和可用性,雖然可用性包括可靠性和可維護(hù)性(Ivezic′,Tanasijevic′,& Ignjatovic′,2008)。因此它可以商定有效性是影響可靠性、可維護(hù)性的功能?？煽啃韵到y(tǒng)不斷的被定義為特征保持操作abilitywithin允許的差異極限在現(xiàn)在;可維護(hù)性的能力是預(yù)防和發(fā)現(xiàn)故障及損壞,系統(tǒng)更新通過參加技術(shù)和操作能力和功能維修,功能實(shí)現(xiàn)功能的程度要求,即調(diào)整環(huán)境,或更準(zhǔn)確系統(tǒng)運(yùn)行的條件。 監(jiān)測的可靠性和可維護(hù)性是常見的監(jiān)控時間的狀態(tài)顯示(圖1)可靠性和可維護(hù)性的函數(shù)可以確定,以及操作的平均時間和平均時間相關(guān)。主要問題出現(xiàn)在形成時間的照片數(shù)據(jù)監(jiān)控和記錄。在現(xiàn)實(shí)條件的機(jī)器應(yīng)該連接到信息系統(tǒng)將準(zhǔn)確記錄每一個失敗、持續(xù)時間和修復(fù)程序。這通常是昂貴或簡易監(jiān)測機(jī)器的性能,即關(guān)閉的,是不精確的。此外,提供的統(tǒng)計數(shù)據(jù)處理時間的狀態(tài)要求所有的機(jī)器在平等的條件下工作,這是難以實(shí)現(xiàn)。至于技術(shù)體系的功能,沒有共同的方法測量和量化。這在本文的原因,為了評估的有效性, 將使用專業(yè)知識和分析機(jī)器判斷工作的工作過程。應(yīng)用專業(yè)知識判斷主要用于文學(xué),主要是為數(shù)據(jù)處理和評估的技術(shù)系統(tǒng)而言:風(fēng)險(Li 廖,2007)、安全(王2000;王、楊、&森1995)或可靠性，用專業(yè)知識判斷自然的語言形式。因此,數(shù)學(xué)和邏輯概念模型進(jìn)行處理的經(jīng)驗(yàn)判斷,即計算的語言描述,模糊集合理論使用(Klir &元,1995;枝,1996)。應(yīng)用模糊今天集代表了最常用的工具之一各領(lǐng)域解決問題的優(yōu)化(黃顧,&杜,2006)和識別(陳,1996)過程問題。Cai(1996)提出了不同的概述應(yīng)用程序方面的模糊方法在系統(tǒng)失敗工程,這是一個接近效能評估問題。應(yīng)用模糊邏輯理論和專家系統(tǒng)(遼、一般2011;Liebowitz,1988)也用于解決優(yōu)化問題的農(nóng)業(yè)機(jī)械領(lǐng)域。(Abbaspour-Fard Rohani & Abdolahpour,2011)的基礎(chǔ)上神經(jīng)網(wǎng)絡(luò)的應(yīng)用程序,在拖拉機(jī)預(yù)測失敗。(Yu,你們&趙,2010)模糊數(shù)學(xué)、可靠性理論和多目標(biāo)優(yōu)化技術(shù)應(yīng)用設(shè)計拖拉機(jī)最終傳動。機(jī)器的可預(yù)測性和可靠性,顯著依賴于其有效性的技術(shù)系統(tǒng)。本文的觀點(diǎn)是根據(jù)模糊集理論的利用率建立模型的有效性。從而說明模糊集是用于分析可靠性、可維護(hù)性和功能表現(xiàn)(部分指標(biāo)的有效性)以及為他們?nèi)谌胄?。他們的工作是以這種有效模型質(zhì)量的方式評估技術(shù)系統(tǒng)。模型可以作為標(biāo)準(zhǔn)購買決策相關(guān)的任何程序,系統(tǒng)的操作或維護(hù),修理的預(yù)測和維護(hù)成本。質(zhì)量和功能的建議模型有效性的確定農(nóng)業(yè)所示機(jī)械、拖拉機(jī)。 2?；谀：挠行员憩F(xiàn)評估理論 數(shù)學(xué)和概念模型的有效性評估實(shí)際上是在兩個步驟:總結(jié)模糊命題的部分的效性指標(biāo);模糊提到的分成一個指標(biāo)——合成。模糊命題過程為代表的聲明,包括語言變量基于可用的信息技術(shù)系統(tǒng)。在這個意義上它必須定義語言的名字變量,代表不同的等級的效果考慮技術(shù)系統(tǒng)和定義的模糊集描述提到的變量。作文是一個模型,它提供了影響結(jié)構(gòu)有效性性能的指標(biāo)。 2.1。模糊模型解決問題 第一步創(chuàng)建的模糊有效性模型(E)評估本身和定義語言變量以及可靠性(R)、可維護(hù)性(M)和功能(F)有關(guān).許多語言變量,它可以發(fā)現(xiàn)最大數(shù)量的理性,人類可辨認(rèn)的表達(dá)式可以同時識別(王et al .,1995)。然而,識別的考慮甚至較小的特征數(shù)量的變量可以有用,因?yàn)閷＜业呐袛?Ivezic′et al .,2008)模糊集的靈活性一般包括過渡現(xiàn)象。根據(jù)以上,五個語言變量為代表的有效性表現(xiàn)包括:窮,充足,平均,和優(yōu)秀。這些語言形式變量給出適當(dāng)?shù)娜悄：?Klir 元,1995),圖2所示。 在圖2中,j = 1,。實(shí)際上,5代表的計量單位有效性。因此,部分指標(biāo)的有效性:R、M和F,隸屬函數(shù)l:在下一步中,執(zhí)行max-min組成。馬克斯-敏成分,也稱為悲觀,經(jīng)常用于模糊代數(shù)作為一個綜合模型(Ivezic′et al .,2008;Tanasijevic et al .,2011;王王et al .,1995;2000)。這個想法是為了讓整體評估(E)等于部分虛擬代表評估。這評估被確定為之間的最好的一個最壞的打算部分成績(R、M或F)。 它可以得出的結(jié)論是,所有的元素(R、M和F)E有同等影響E,max-min組成以并行方式被使用,這將部分的到綜合指標(biāo)。在文學(xué)(Ivezic′et al .,2008;etal .,1995)max-min成分通過運(yùn)營商”和“和”或“提供一個優(yōu)勢在其他的某些元素在合成的過程中,也使用。 準(zhǔn)確地說,如果我們看看三個部分指標(biāo),即他們的隸屬函數(shù)(1),可以使C:= j3 = 53組合 的隸屬度函數(shù)。每一種組合代表一個可能的合成效果評估(E)。 這個表達(dá)式(6)有必要映射回E模糊集(圖2)。最佳(王et al .,1995),用于轉(zhuǎn)換方法E描述(6)形成定義等級的會員模糊集:貧窮、充足,平均,和優(yōu)秀的好。這個過程被公認(rèn)為識別。最佳方法是使用距離E(d)之間通過“max-min”成分(6)和每個人E表達(dá)式(根據(jù)圖2)來表示的程度E是確認(rèn)每個模糊集的有效性(圖2)。越接近勒(6)是第i個語言變量,小迪。距離di等于零,如果勒(6)只是第i個相同隸屬度函數(shù)的表達(dá)式。在這種情況下,E不應(yīng)該評估其他表達(dá)式,由于這些表達(dá)式的排他性。假設(shè)迪民(i = 1,。,5)是最小的距離對Ej,讓a1,。,a5代表相對的倒數(shù)距離(計算相應(yīng)的比率距離di(7)和迪民提到的值)。然后,人工智能 : 1.一個說明性的例子 作為一個說明性的例子對農(nóng)業(yè)機(jī)械的評價有效性,比較分析三個拖拉機(jī)A1 B2、本文給出和C2。 在拖拉機(jī)7.146 l發(fā)動機(jī)LO4V TCD 2013安裝。謝謝從35%的扭矩儲備,拖拉機(jī)是能夠滿足所有需求預(yù)期表現(xiàn)最差的農(nóng)業(yè)操作在農(nóng)業(yè)?？偼侠瓩C(jī)質(zhì)量是16000公斤。根據(jù)經(jīng)濟(jì)合作與發(fā)展組織(代碼2)報告最大動力輸出軸功率測量在2200轉(zhuǎn)243千瓦的燃油消耗率嗎198 g /千瓦小時(ECE-R24)。發(fā)動機(jī)的最大扭矩1482海里在引擎1450 rpm的政權(quán)。傳動裝置是精心“不一樣的”傳達(dá)。事業(yè)聯(lián)動機(jī)制是一個類別II / III與提升11800公斤。 在拖拉機(jī)B2和C2 8.134 l發(fā)動機(jī)6081 hrw37 JD安裝,儲備扭矩的40%,這能夠滿足所有的拖拉機(jī)需求預(yù)期表現(xiàn)最差的農(nóng)業(yè)在農(nóng)業(yè)操作。拖拉機(jī)總重量是14000公斤。根據(jù)經(jīng)合組織(代碼2)報告最大的權(quán)力來衡量動力輸出軸在2002轉(zhuǎn)217千瓦燃料消耗率193克/千瓦小時(ECE-R24)。在發(fā)動機(jī)最大扭矩1320海里轉(zhuǎn)速為1400 rpm。傳播是“AutoPower。聯(lián)動機(jī)制是一個類別II / III 10790丹的提升力。 兩個模型都是電子控制拖拉機(jī)發(fā)動機(jī)和燃料供給系統(tǒng),滿足排放法規(guī)。從提交的技術(shù)特點(diǎn)的拖拉機(jī),B和C看到所有三個拖拉機(jī)全功能forperforming困難操作不同的農(nóng)業(yè)技術(shù)生產(chǎn)。拖拉機(jī)B和C有相同的技術(shù)特征,和實(shí)踐是相同的類型和模式,除了拖拉機(jī)B進(jìn)入操作在2007年5月,一輛拖拉機(jī)C 6月2007年。一輛拖拉機(jī)實(shí)驗(yàn)農(nóng)場,這是技術(shù)文檔的基本模型,在7月份進(jìn)入操作2009年。保持農(nóng)業(yè)技術(shù)的主要任務(wù)提供功能和機(jī)器的可靠性。維護(hù)所有三個拖拉機(jī)是通過機(jī)器商店所擁有的用戶升級選擇。 十個工程師(分析師)致力于維護(hù)和操作拖拉機(jī)的采訪。他們評價R,D和F表1中給出。首先,拖拉機(jī)是計算的有效性?？梢钥闯隹煽啃允怯墒姆治鰩熢u為優(yōu)秀(6/10 = 0.6),平均三(0.3)和一樣好(0.1)。以這種方式獲得評估R在表單中，在下一步中,這些評估是映射在模糊集(圖1)為了獲得評估(1)。例如,可靠性在這個例子中確定(11),它是語言0.6變量優(yōu)秀加入重量。 因此,模糊集優(yōu)秀定義為:Rexc=(1/0,1/0,1/0,4/0.25 5/1.0)(據(jù)嗎圖1)。這樣的特定的值模糊集優(yōu)秀Rexc0.6 =(1 / 0.6(0),2 / 0.6(0),3 / 0.6(0),4 /(0.25 - 0.6),5 /(1.0 - 0.6)}。剩下的四個語言變量被以同樣的方式對待。最后對于每個j = 1,。5具體隸屬度函數(shù)(最后一行,表2)被添加到最后拖拉機(jī)可靠性模糊形式(1):這些fuzzificated評估(11)和(12)是合成所必需的評估的有效性,使用max-min邏輯。在這種情況下可以使C = 53 = 125組合,走出48的結(jié)果。 第一個結(jié)果是組合2-2-3:E2-2-3(0.025,0.05,0.125),哪里X2-2-3 =(2 + 2 + 3)/ 3 = 2(四舍五入為整數(shù))。最小值的隸屬度函數(shù)這一結(jié)果的是0.025。其他的結(jié)果和相應(yīng)的我的值如表3所示。所有這些結(jié)果都可以圍繞尺寸X = 2、3、4和5。拖拉機(jī)在很大程度上為0.30065(與30%)評估那么好,拖拉機(jī)在很大程度上0.27538(27.5%)評估一樣好,而拖拉機(jī)C在很大程度上為0.25468平均(25.5%)評估。它可以得出的結(jié)論是,C是最糟糕的,當(dāng)拖拉機(jī)只是稍微比B,特別是如果我們看到的評估為優(yōu)秀的28.8%,而B的程度23.8%的程度。分析了拖拉機(jī)可以提出的有效性如圖3。,它可以更清楚地看到,拖拉機(jī)的最大的效果。如果這個評估(EA,EB,EC)defuzzificated是重心點(diǎn)計算- Z(Bowles & Pelaez,1995),我們得到了評估的效果如下: 這就意味著在1 - 5(即從貧困的規(guī)模優(yōu)秀)拖拉機(jī)是最好的和拖拉機(jī)C是最壞的打算。驗(yàn)證的實(shí)現(xiàn)結(jié)果,統(tǒng)計分析的可用性,像家庭與有效性概念,已經(jīng)被使用。那在我們的模型顯示,拖拉機(jī)是最好的,和C的壞的效果。在現(xiàn)實(shí)中,如果我們分析的可用性,它是看到2904 moto-hours拖拉機(jī)在工作3130年可用moto-hours;如果10000 moto-hours計算,在9244年的工作將花費(fèi)moto-hours。拖拉機(jī)B的10004年moto-hours可用,它花9069moto-hours在工作,和拖拉機(jī)C 9981可用moto-hours花了9045年的工作。實(shí)驗(yàn)表明,更可靠和有效的拖拉機(jī)是少是延遲。在某種程度上,這個初始的優(yōu)勢消滅更糟糕的物流交付備件的時候涉及到拖拉機(jī),拖拉機(jī)a . 1100年moto-hours工作可憐的物流在維護(hù)希望8個工作日, 一個給定的拖拉機(jī)和它極大地影響了可維護(hù)性的下降帶來的好處,因此相同的效率(內(nèi)部技術(shù)PKB)總剝削的下降。 1.結(jié)論 本文提出一種模型有效性的評估技術(shù)系統(tǒng)、精確農(nóng)業(yè)機(jī)械、基于模糊集理論。表現(xiàn)作為整體的有效性指標(biāo)系統(tǒng)的服務(wù)質(zhì)量,即為整個測量技術(shù)系統(tǒng)的可用性。可靠性、可維護(hù)性和功能表演已經(jīng)公認(rèn)的有效性參數(shù)或指標(biāo)。語言可以被任命為形式所有提到的共同特征指標(biāo)。因此模糊集理論出現(xiàn)自然工具建模的有效性。在本文中,應(yīng)用模糊集理論,這是必要的定義:語言變量及其描述隸屬函數(shù)、模糊規(guī)則的組成和模型集成和去模糊化。模糊的成分即max-min邏輯已經(jīng)被用于集成的有效性指標(biāo)有效性的整體性能,最適合集成的方法模糊集的隸屬函數(shù)和質(zhì)心點(diǎn)去模糊化的模糊數(shù)的計算數(shù)值。Max-min組合模型,它暴露在這篇文章中,沒有以這種方式處理相應(yīng)的文獻(xiàn)。另外,在案例研究中,模型的模糊化的問卷調(diào)查的結(jié)果,它代表的正是所積累的方式工程師的知識和技能。 提出的模型可以作為一個簡單的工具的快速估計的有效性即為農(nóng)業(yè)服務(wù)的質(zhì)量機(jī)械、基于專家判斷和估計。在同時,該模型不需要復(fù)雜的IT基礎(chǔ)設(shè)施。分析實(shí)現(xiàn)模糊集和適當(dāng)?shù)哪：行钥煽啃浴⒖删S護(hù)性和功能表現(xiàn)可以糾正措施的指導(dǎo)購買的方向嗎的設(shè)備,結(jié)構(gòu)調(diào)整,改變的維護(hù)政策或管理/運(yùn)營商變更 本文具體分析了三個拖拉機(jī),標(biāo)志著一個B和C,這表明更高效的拖拉機(jī)越頻繁宕機(jī)。在某種程度上,這種最初的優(yōu)勢就終止了窮交付備件物流。 感謝 研究工作得到了塞爾維亞共和國教育部和科學(xué)界的支持。 Effectiveness assessment of agricultural machinery based on fuzzy sets theoryRajko Miodragovic a, Milo Tanasijevic b, Zoran Mileusnic a, Predrag Jovanc ic baUniversity of Belgrade, Faculty of Agriculture, SerbiabUniversity of Belgrade, Faculty of Mining and Geology, Serbiaa r t i c l ei n f oKeywords:Agricultural machineryEffectivenessFuzzy setMaxmin compositiona b s t r a c tThe quality of service of agricultural machinery represents one of the basic factors for successful agricul-tural production. In this sense, there is a clear need for defining the exact indicator of the quality of thesemachines, according to which it could be possible to determine which machine is optimal for differentworking conditions. The concept of effectiveness represents one of synthesis indicators of the qualityof service of the technical systems. In this paper the effectiveness is defined using the fuzzy set theory,and reliability, maintainability and functionality are used as influence indicators of the effectiveness.In that sense the model for assessing the effectiveness of tractor as a typical representative of agromachinery has been formed. The model is based on integration of linguistic description of the above men-tioned influence indicators using fuzzy set theory and maxmin composition. The model was tested onthe example of three tractors of the same category, which are exploited in climatic and soil conditionsin the wider Belgrade (Serbia) area. Even if the conditions in this experiment were approximately equal,the difference of the achieved effects was attained and very significant, compared to other operationparameters.? 2012 Elsevier Ltd. All rights reserved.1. IntroductionRapid expansion of global demands for agricultural products hascaused much greater development of agricultural technique, apro-pos machines and equipments. It is widely recognized that contem-porary agricultural systems demand careful and detailed planningand control of all relevant biological, technical, technological andother processes. An accurate and reliable predicting of the final out-come for each specified operation, as well as for the complete cropproductionprocess,isofspecialimportance.Demandshaveintensi-fied the introduction of sophisticated experimental, mathematical,statistical, mechanical and other methods in agricultural sciencesduring the last few decades. Besides the demands described above,anadequatetechnicalsystemhastosatisfythecriteriaofproductiv-ity, imposed by the conditions of desired crop production. In mostcases, the capacity of tractor-machinery systems on farms in Serbiais much over the optimal level (Nikolic , 2005), increasing the costsof crop production.Nowadays, the existing mathematical optimiza-tion methods, supported by the high-performance computers, canefficiently resolve the optimization problems (Dette & Weber,1990; Duffy et al., 1994; Mileusnic , 2007; etc.). The formation ofan optimal technical system in order to produce cheaper food,highly impacted reliability of tractors, its maintainability, and thefunctionality of the system.With the beginning of systems sciences development, practicallyafter the II World War, in appropriate engineering and scientific liter-ature a series of concepts have been defined, with the idea to describeessential characteristics of technical systems from the point of theirquality of service. Reliability as the indicator of technical systembehaviors in operation, and maintainability as the indicator of techni-cal system behaviors during the period of failures can be stated as themost recognizable concepts. These two concepts and their implemen-tations had the most progressive development. The concept of effec-tiveness was defined later in attempt to describe simultaneouslytechnicalsystemsbehaviorsinoperationandinperiodsoffailure.Thisconceptconsideredreliabilityandavailabilityperformances,aswellasfunctionalityofproposedtechnicalsystemdesign(Papic&Milovanovic,2007). In other words, the effectiveness of a technical system can bearticulatedasprobabilitythatatechnicalsystemwillbeputinfunc-tionsuccessfullyand performrequiredcriterionfunctionwithinthelimits of allowed discrepancies for given time period and given sur-rounding conditions. Although in the same spirit, some authors havedefined effectiveness somewhat differently. In (Ebramhimipour &Suzuki, 2006) effectiveness was defined as overall indicator whichcontains efficiency, reliability and availability. These two citeddefinitionsinclude parallelconcerningofreliabilityandavailability,althoughavailabilityincludesreliabilityandmaintainability(Ivezic ,Tanasijevic ,&Ignjatovic ,2008).Thereforeitcanbeagreeduponthatthe effectivenessis influenced by reliability, maintainability and func-tionality. Reliability is defined as characteristic of a system to contin-uouslykeepoperatingabilitywithinthelimitsofalloweddiscrepancies0957-4174/$ - see front matter ? 2012 Elsevier Ltd. All rights reserved.doi:10.1016/j.eswa.2012.02.013Corresponding author.E-mail address: tanrgf.bg.ac.rs (M. Tanasijevic ).Expert Systems with Applications 39 (2012) 89408946Contents lists available at SciVerse ScienceDirectExpert Systems with Applicationsjournal homepage: the calendar period of time; maintainability as capacity of thesystemforpreventionandfindingfailuresanddamages,forrenewingoperating ability and functionality through technical attending andrepairs; and functionality as the degree of fulfilling the functionalrequirements, namely the adjustment to environment, or more pre-cisely to the conditions in which the system operates.In the case of monitoring reliability and maintainability it iscommon to monitor the time picture of state (Fig. 1) according towhich the functions of reliability and maintainability can be deter-mined, as well as the mean time in operation and the mean time infailure.The main problem that occurs in forming the time picture ofstate is data monitoring and recording. In real conditions the ma-chines should be connected to information system which wouldprecisely record each failure, duration and procedure of repair. Thisis usually expensive and improvised monitoring of the machineperformance, namely of its shut downs, is imprecise. Moreover,statistical data processing provided by the time picture of the staterequires that all machines work under equal conditions, which isdifficult to achieve. As for the functionality of the technical system,there is no common way for its measuring and quantification. Thisis the reason why in this paper, in order to assess the effectiveness,expertise judgments of the employed in the working process of theanalyzedmachineswillbeused.Applicationofexpertisejudgments has been largely used in literature, primarily for dataprocessing and the assessment of the technical systems in termsof: risk (Li & Liao, 2007), safety (Wang 2000; Wang, Yang, & Sen,1995) or dependability (Ivezic et al., 2008; Tanasijevic, Ivezic,Ignjatovic, & Polovina, 2011). Expertise judgment is naturally givenin linguistic form. Thereby, as the logical mathematical andconceptual model for processing the expertise judgments, namelyfor calculating with linguistic descriptions, the fuzzy set theorywas used (Klir & Yuan, 1995; Zadeh, 1996). Application of fuzzysets today represents one of the most frequently used tools forsolving the problems in various areas of optimization (Huang,Gu, & Du, 2006) andidentification (Chan, 1996) regardingengineering problems. Cai (1996) presents the overview of variousapplication aspects of fuzzy methodology in systemfailureengineering, which is a problem close to effectiveness assessment.Application of fuzzy logic theory and experts systems (Liao,2011; Liebowitz, 1988) in general is also used for solving theoptimizations problems from area of agro machinery. In article(Rohani, Abbaspour-Fard, & Abdolahpour, 2011) on the base ofneural networks application, failures on tractors were predicted.In article (Ye, Yu, & Zhao, 2010) fuzzy mathematics, reliabilitytheory and multi-objective optimization technology were appliedto design tractors final transmission. Predictability of machinedowntimes and reliability, significantly depends on its effective-ness of technical systems.The idea of this paper is to establish the model for effectivenessdetermination according to fuzzy sets theory utilization. Therebythe fuzzy sets were used to analyze reliability, maintainabilityand functionality performances (partial indicators of effectiveness)as well as for their integration into effectiveness. In this way effec-tive model for the quality assessment of the technical systems intheir working conditions is obtained. The model can be used as cri-teria for decision making related to any procedure in purchasing,operation or maintenance of the system, for prediction of repairand maintenance costs. Quality and functionality of the proposedmodel is shown in effectiveness determination of agriculturalmachinery, precisely tractors.2. Effectiveness performance assessment based on fuzzy setstheoryMathematical and conceptual model of effectiveness assess-ment is practically summarized in two steps: fuzzy propositionof effectiveness partial indicators; and fuzzy composition of men-tioned indicators into one synthesized. Fuzzy proposition is pro-cedure for representing the statement that includes linguisticvariables based on available information about considered techni-cal system. In that sense it is necessary to define the names of lin-guistic variables that represent different grades of effectiveness ofconsidered technical system and define the fuzzy sets that describethe mentioned variables. Composition is a model that providesstructure of indicators influences to the effectiveness performance.2.1. Fuzzy model of problem solvingThe first step in the creation of fuzzy model for effectiveness (E)assessment is defining linguistic variables related to itself and toreliability (R), maintainability (M) and functionality (F). Regardingnumber of linguistic variables, it can be found that seven is themaximal number of rationally recognizable expressions that hu-man can simultaneously identify (Wang et al., 1995). However,for identification of considered characteristics even the smallernumber of variables can be useful because flexibility of fuzzy setsto include transition phenomena as experts judgments commonlyis (Ivezic et al., 2008). According to the above, five linguistic vari-ables for representing effectiveness performances are included:poor, adequate, average, good and excellent. Form of these linguis-tic variables is given as appropriate triangular fuzzy sets (Klir &Yuan, 1995), and they are presented in Fig. 2.In Fig. 2, j = 1,.,5 practically represents measurement units ofeffectiveness.Thereby, partial indicators of effectiveness: R, M and F, pre-sented as membership functionl:lR l1R;.;l5R;lM l1M;.;l5M;lF l1F;.;l5F1In the next step, maxmin composition is performed on them. Maxmin composition, also called pessimistic, is often used in fuzzy alge-bra as a synthesis model (Ivezic et al., 2008; Tanasijevic et al., 2011;Wang et al., 1995; Wang 2000). The idea is to make overall assess-ment (E) equal to the partial virtual representative assessment. Thisassessment is identified as the best possible one between the worstpartial grades expected (R, M or F).It can be concluded that all elements of (R, M and F) that makethe E have equal influence on E, so that maxmin composition willbe used, which in parallel way treats the partial ones onto theFig. 1. Time picture of state, t time spent in operation,s time in failure, h time of planned shut down due to preventive maintenance.R. Miodragovic et al./Expert Systems with Applications 39 (2012) 894089468941synthetic indicator. In literature (Ivezic et al., 2008; Wang et al.,1995) maxmin compositions which by using operators ANDand OR provide an advantage to certain elements over the othersin the process of synthesis, are also used.Precisely, if we look at three partial indicators, namely theirmembership function (1), it is possible to make C = j3= 53combina-tions of their membership functions. Each of these combinationsrepresents one possible synthesis effectiveness assessment (E).E lj1;.;5R;lj1;.;5M;.;lj1;2;.5Fhi;for all c 1 to C2If we take into account only values iflj1;.;5R;M;F 0, we get combina-tions that are named outcomes (o = 1 to O, where O # C).Further, for each outcome its values are calculated (Xc). Theoutcome which would suit the combination c, it would be calcu-lated following the equations:XcPR;M;Ejhic33Finally, all of these outcomes are treated with maxmin composi-tion, as follows:(i) For each outcome search for the MINimum value oflR,M,Finvector Ec(2). The minimum which would suit the combina-tion o, it would be calculated following the equations:MIN0 minflj1;.;5R;lj1;.;5M.;lj1;.;5Fg;for all o 1 to O4(ii) Outcomes are grouped according to their valuesXc(3),namely the size of j.(iii) Find the MAXimum between previously identified mini-mums (i) for each group (ii) of outcomes. The maximumwhich would suit value of j, would be calculated followingthe equations:MAXj maxfMINog; for every j5E assessment of technical system is obtained in the form:lE MAXj1;.;MAXj5 l1E;.;l5E6This expression (6) is necessary to map back to the E fuzzy sets(Fig. 2). Best-fit (Wang et al., 1995), method is used for transforma-tion of E description (6) to form that defines grade of membershipto fuzzy sets: poor, adequate, average, good and excellent. This pro-cedure is recognized as identification. Best-fit method uses distance(d) between E obtained by maxmin composition (6) and each ofthe E expressions (according to Fig. 2), to represent the degree towhich E is confirmed to each of fuzzy sets of effectiveness (Fig. 2).diEj;Hi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX5j1ljE ?ljHj2vuut;j 1;.;5;Hi fexcellent;goodaverage;adequate;poorg7where is (according to Fig. 2):lexc.= (0,0,0,0.25,1);lgood= (0,0,0.25,1,0.25);laver.= (0,0.25,1,0.25,0);ladeq.= (0.25,1,0.25,0,0);lpoor= (1,0.25,0,0,0).The closerlE(6) is to the ith linguistic variable, the smaller diis.Distance diis equal to zero, iflE(6) is just the same as the ithexpression in terms of the membership functions. In such a case,E should not be evaluated to other expressions at all, due to theexclusiveness of these expressions.Suppose dimin(i = 1,.,5) is the smallest among the obtaineddistances for Ejand leta1,.,a5represent the reciprocals of the rel-ative distances (which is calculated as the ratio between corres-ponding distance di(7) and the mentioned values dimin). Then,aican be defined as follows:ai1di=dimin;i 1;.;58If di= 0 it follows thatai= 1 and the others are equal to zero. Then,aican be normalized by:biajP5m1aim;i 1;.;5X5i1bi 19Each birepresents the extent to which E belongs to the ith defined Eexpressions. It can be noted that if Eicompletely belongs to the ithexpression then biis equal to 1 and the others are equal to 0. Thus bjcould be viewed as a degree of confidence that Eibelongs to the ith Eexpressions. Final expression for E performance at the level of tech-nical system, have been obtained in the form (10)Eifbi1;poor;bi2;adequate;bi3;good;bi4;average;bi5;excellentg103. An illustrative exampleAs an illustrative example of evaluation of agriculture machin-ery effectiveness, the comparative analysis of three tractors A1B2,and C2is given in this article.In tractor A a 7.146 l engine LO4V TCD 2013 is installed. Thanksto the reserves of torque from 35%, the tractor is able to meet allthe requirements expected in the worst performing farming oper-ations in agriculture. Total tractor mass is 16,000 kg. According toOECD (CODE II) report maximum power measured at the PTO shaftis243 kWat2200 rpmwithspecificfuelconsumptionof198 g/kW h (ECE-R24). Maximum engine torque is 1482 Nm at en-gine regime of 1450 rpm. Transmission gear is vario continioustransmision. Linkage mechanism is a Category II/III with liftingforce of 11,800 daN.In tractors B2and C28.134 l engine 6081HRW37 JD is installed,with reserve torque of 40%, and this tractor was able to meet all therequirements expected in the worst performance of the farmingoperations in agriculture. Total tractor weight is 14,000 kg. Accord-ing to OECD (CODE II) report maximum power measured at thePTO shaft is 217 kW at 2002 rpm with specific fuel consumptionof 193 g/kW h (ECE-R24). Maximum torque is 1320 Nm at enginerevs of 1400 rpm. Transmission is AutoPower. Linkage mechanismis a Category II/III with lifting force of 10,790 daN.Both models have electronically controlled tractor engine andfuel supply system that meets the regulations on emissions.From the submitted technical characteristics of the tractor A, Band C it is seen that all three tractors are fully functional forFig. 2. Effectiveness fuzzy sets.1Tractor Fendt Vario 936.2Tractor John Deere 8520.8942R. Miodragovic et al./Expert Systems with Applications 39 (2012) 89408946performing difficult operations for different technologies of agri-cultural production. Tractors B and C have the same technical char-acteristics, and practice is the same type and model, except thatthe tractor B entered into operation in May 2007, a tractor C in June2007. A tractor on the experimental farm, which is the technicaldocumentation for the base model, comes into operation in July2009. The main task of maintaining agricultural techniques is toprovide functionality and reliability of machines. Maintenance ofall three tractors is done by machine shop owned by the user up-grade option.Ten engineers (analysts) working on maintenance and opera-tion of tractors were interviewed. Their evaluation of R, D and Fare given in Table 1.First, the effectiveness of tractor A is calculated. It can be seenthat the reliability was assessed as excellent by six out of ten ana-lysts (6/10 = 0.6), as average by three (0.3) and as good by one(0.1). In this way the assessment R is obtained in the form (11):R 0:6=exc; 0:3=good; 0:1=aver; 0=adeq; 0=poor11In the same way the assessments for M and F are obtained:M 0:4=exc; 0:4=good; 0:2=aver; 0=adeq; 0=poorF 0:5=exc; 0:5=good; 0=aver; 0=adeq; 0=poorIn the next step, these assessments are mapped on fuzzy sets (Fig. 1)in order to obtain assessment in the form (1). For example, Reliabil-ity in this example is determined as (11), where it is to linguisticvariable excellent joined weight 0.6. Thereby, fuzzy set excellentis defined as: Rexc= (1/0, 2/0, 3/0, 4/0.25, 5/1.0) (according toFig. 1). In this way the specific values of fuzzy set excellentRexc0.6= (1/(0 ? 0.6),2/(0 ? 0.6),3/(0 ? 0.6),4/(0.25 ? 0.6),5/(1.0 ? 0.6) are obtained. The remaining four linguistic variablesare treated in the same way. In the end for each j = 1,.,5 specificmembership functions (last row, Table 2) are added into the finalfuzzy form (1) of tractor A reliability:lRA 0;0:025;0:175;0:475;0:675In the same way, based on the questionnaire (Table 1) values formaintainability and functionality are obtained:lMA 0;0:05;0:3;0:55;0:5;lFA 0;0;0:125;0:625;0:62512These fuzzificated assessments (11) and (12) are necessary to syn-thesize into assessment of effectiveness, using maxmin logics. Inthis case it is possible to make C = 53= 125 combinations, out ofwhich the 48 outcomes. First outcome would be for combination2-2-3: E2-2-3= 0.025,0.05,0.125, where isX2-2-3= (2 + 2 + 3)/3 = 2(rounded as integer). Smallest value among the membership func-tions of this outcome is 0.025. Other outcomes and correspondingvalues ofXcare shown in Table 3. All these outcomes can begrouped around sizesX= 2, 3, 4 and 5.For example, for outcomeX= 5 it can be written:E4?5?5 0:475;0:5;0:625?;E5?4?5 0:675;0:55;0:625?;E5?5?4 0:675;0:5;0:625?;E5?5?5 0:675;0:5;0:625?Further, for each of them, minimum between membership functionis sought:Table 1Results of questionnaire.AnalystLinguistic variablesTractor ATractor BTractor CExcellentGoodAverageAdequatePoorExcellentGoodAverageAdequate