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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: /locate/eswaduring 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 CExcellentGoodAverageAdequatePoorExcellentGoodAverageAdequatePoorExcellentGoodAverageAdequatePoor1RxxxMxxxFxxx2RxxxMxxxFxxx3RxxxMxxxFxxx4RxxxMxxxFxxx5RxxxMxxxFxxx6RxxxMxxxFxxx7RxxxMxxxFxxx8RxxxMxxxFxxx9RxxxMxxxFxxx10RxxxMxxxFxxxR. Miodragovic et al./Expert Systems with Applications 39 (2012) 894089468943MINE4?5?5 minf0:475;0:5;0:625g 0:475;MINE5?4?5 0:55;MINE5?5?4 0:5;MINE5?5?5 0:5Between these minimums, in the end it seeks maximum:MAXXd5 maxf0:475;0:55;0:5;0:5g 0:55Also for other values:X: MAXX= 2= 0.025; MAXX= 3= 0.175;MAXX= 4= 0.55 (Table 1.)Finally, we get expression for membership function of effective-ness of tractor A:lEA 0;0:025;0:175;0:55;0:55Best-fit method (79) and proposed E fuzzy set (Fig. 1) give the finaleffectiveness assessment for the tractor A:d1E;excffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX5j1ljE?ljexc2vuutffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0?020:025?020:175?020:55?0:2520:55?12q0:56899where is :lE 0;0:025;0:175;0:55;0:55lexc 0;0;0;0:25;1Forotherfuzzysets:d2(E,good) = 0.54658,d3(E,aver) = 1.06007, d4(E, adeq) = 1.27426, d5(E, poor) = 1.29856.for dmin d2:a11d1=d210:56899=0:54658 0:96061;a2 1:00000;a3 0:51561;a4 0:42894;a5 0:42091:b1a1P5i1ai0:969010:96901 1 0:51561 0:42894 0:42091 0:28881;b2 0:30065;b3 0:15502;b4 0:12896;b5 0:12655:Finally, we get the assessment of effectiveness of tractor A, inform (10):EA= (b1, excellent), (b2, good), (b3, average), (b4, ade-quate),(b5,poor) = (0.28881,excellent),(0.30065,good),(0.15502,average),(0.12896,adequate),(0.12655, poor)In the same way, we get the assessments for other two tractorsB and C:EB= (0.23793, excellent), (0.27538, good), (0.20635, aver-age), (0.14693, adequate), (0.13342, poor)EC= (0.17507, excellent), (0.25092, good), (0.25468, aver-age), (0.17633, adequate), (0.14300, poor).Tractor A is in great extent of 0.30065 (in relation to 30 %) as-sessed as good, tractor B in great extent of 0.27538 (27.5%) as-sessed as good, while tractor C is in great extent of 0.25468(25.5%) assessed as average. It can be concluded that C is the worst,while tractor A is only somewhat better than B, especially if we seeTable 2Calculation of specific values of fuzzy sets.123450.6/exc.0 ? 0.60 ? 0.60 ? 0.60.25 ? 0.61.0 ? 0.60.3/good0 ? 0.30 ? 0.30.25 ? 0.31.0 ? 0.30.25 ? 0.30.1/aver.0 ? 0.10.25 ? 0.11.0 ? 0.10.25 ? 0.10 ? 0.10/adeq.0.25 ? 01.0 ? 00.25 ? 00 ? 00 ? 00/poor1.0 ? 00.25 ? 00 ? 00 ? 00 ? 0PR00.0250.1750.4750.675Table 3Structure of MAXMIN composition.Comb.XlMIN23452-2-320.025,0.05,0.1250.0252-2-430.025,0.05,0.6250.0252-2-530.025,0.05,0.6250.0252-3-330.025,0.3,0.1250.0252-3-430.025,0.3,0.6250.0252-3-530.025,0.3,0.6250.0252-4-330.025,0.55,0.1250.0252-4-430.025,0.55,0.6250.0252-4-540.025,0.55,0.6250.0252-5-330.025,0.5,0.1250.0252-5-440.025,0.5,0.6250.0252-5-540.025,0.5,0.6250.0253-2-330.175,0.05,0.1250.053-2-430.175,0.05,0.6250.053-2-530.175,0.05,0.6250.053-3-330.175,0.3,0.1250.1253-3-430.175,0.3,0.6250.1753-3-540.175,0.3,0.62500.1753-4-330.175,0.55,0.1250.1253-4-440.175,0.55,0.6250.1753-4-540.175,0.55,0.6250.1753-5-340.175,0.5,0.1250.1253-5-440.175,0.5,0.6250.1753-5-540.175,0.5,0.6250.1754-2-330.475,0.05,0.1250.054-2-430.475,0.05,0.6250.054-2-540.475,0.05,0.6250.054-3-330.475,0.3,0.1250.1254-3-440.475,0.3,0.6250.34-3-540.475,0.3,0.6250.34-4-340.475,0.55,0.1250.1254-4-440.475,0.55,0.6250.4754-4-540.475,0.55,0.6250.4754-5-340.475,0.5,0.1250.1254-5-440.475,0.5,0.6250.4754-5-550.475,0.5,0.6250.4755-2-330.675,0.05,0.1250.055-2-440.675,0.05,0.6250.055-2-540.675,0.05,0.6250.055-3-340.675,0.3,0.1250.1255-3-440.675,0.3,0.6250.35-3-540.675,0.3,0.6250.35-4-340.675,0.55,0.1250.1255-4-440.675,0.55,0.6250.555-4-550.675,0.55,0.6250.555-5-340.675,0.5,0.1250.1255-5-450.675,0.5,0.6250.55-5-550.675,0.5,0.6250.5MAX0.0250.1750.550.558944R. Miodragovic et al./Expert Systems with Applications 39 (2012) 89408946that A is assessed as excellent in the extent of 28.8% while B in theextent of 23.8%. Effectiveness of analyzed tractors can be presentedas in Fig. 3., where it can be more clearly seen that tractor A has thebiggest effectiveness.If this assessment (EA, EB, EC) is defuzzificated by center of masspoint calculation Z (Bowles & Pelaez, 1995), we get the assess-ment of effectiveness as follows:ZAP5i1bi?CiP5i1bi0:28881?50:30065?40:15502?30:12896?20:12655?10:288810:300650:155020:128960:126553:50 ZB3:34 and ZC3:14where C is numerical equivalent for linguistic variables (poor = 1,adequate = 2.)This would mean that on the scale of 15 (i.e. from poor toexcellent) tractor A is the best and tractor C is the worst.For verification of achieved results, statistical analysis of avail-ability, like family concept with effectiveness, has been used. Thatis, in our model showed that the tractor A is of a best, and C ofworst effectiveness. In reality, if we analyze the availability, it isseen that the tractor A spent in work 2904 moto-hours, outof 3130 available moto-hours; if calculated on 10,000 moto-hours,it would spend in work 9244 moto-hours. As of the tractor B, out of10,004 available moto-hours, it spent 9069 moto-hours in work,and tractor C out of 9981 available moto-hours spent 9045 in work.The experiment showed that the more reliable and efficienttractors are the less frequent are delays. In part, this initial advan-tage wiped out worse logistics of delivery of spare parts when itcomes to tractor A. in 1100 moto-hours work of the tractor, dueto poor logistics in maintaining hoped to eight working days, andit greatly influenced the decline in benefits of maintainability ofa given tractor and thus the decline in total exploitation of thesame efficiency (Internal technical documentation PKB).4. ConclusionThis paper presents a model for effectiveness assessment oftechnical systems, precisely agricultural machinery, based on fuzzysets theory. Effectiveness performance has been adopted as overallindicator of systems quality of service, i.e. as entire measure oftechnical system availability. Reliability, maintainability and func-tionality performances have been recognized as effectivenessparameters or indicators. Linguistic form can be appointed as thecommon characteristics of all mentioned indicators. Therefore fuz-zy sets theory has appeared as natural tool for effectiveness mod-eling. In this article, for application of fuzzy set theory, it wasnecessary to define: linguistic variables and their description bya membership function, rules of fuzzy composition and models ofintegration and defuzzification. Fuzzy composition i.e. maxminlogic has been used for integration of effectiveness indicators inthe overall effectiveness performance, best fit method for integra-tion of membership function in fuzzy set and center of mass pointcalculation for defuzzification of fuzzy number in numeric values.Maxmin composition model, which is exposed in this paper, hasnot been processed in this way in corresponding literatures. Also,in case study, the model of fuzzification of results of questionnaireis presented, which represent precisely shown way of accumula-tion of engineer knowledge and expertise.Presented model can be used as a simple tool for the fast esti-mation of effectiveness i.e. quality of service for agriculturalmachinery, based on experts judgments and estimations. At thesame time, the model does not require a complex IT infrastructure.Analysis of achieved effectiveness fuzzy sets and appropriate fuzzysets for reliability, maintainability and functionality performancescan be the guideline for corrective actions in the directions of pur-chase of equipment, construction adjustment, changing of mainte-nance policy or management/operators alteration.The paper specifically analyzes the three tractors, marked A, Band C, which showed that the more efficient tractors the less fre-quent downtimes. In part, this initial advantage is annulled poorerdelivery of spare parts logistics.AcknowledgementThe research work is supported by the Ministry of Educationand Science of the Republic of Serbia.ReferencesBowles, J. B., & Pelaez, C. E. (1995). Fuzzy logic prioritization of failures in a systemfailure mode, effects and criticality analysis. 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