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摘要在人力管理理論、實(shí)踐的深入發(fā)展下,這讓人力管理工作成為了現(xiàn)代企業(yè)的標(biāo)配,同時(shí)也是一項(xiàng)核心工作。創(chuàng)立企業(yè),是為了發(fā)展獲利,而當(dāng)下的市場(chǎng)日益飽和,許多行業(yè)都進(jìn)入到了存量市場(chǎng)的競(jìng)爭(zhēng)當(dāng)中,所以,企業(yè)需利用創(chuàng)新來(lái)驅(qū)動(dòng)發(fā)展,而創(chuàng)新發(fā)展的關(guān)鍵在于人才,此時(shí)也就凸顯出了績(jī)效考核管理制度的重要性,其是現(xiàn)代企業(yè)管理的科學(xué)手段,有利于激發(fā)員工的創(chuàng)新創(chuàng)造發(fā)展,從而驅(qū)動(dòng)企業(yè)的創(chuàng)新發(fā)展。現(xiàn)階段,因?yàn)閲?guó)內(nèi)的管理實(shí)踐整體比較滯后,此時(shí)國(guó)內(nèi)雖然有不少企業(yè)開(kāi)展了績(jī)效考核工作,然而,取得預(yù)期效果的非常少,這制約著國(guó)內(nèi)企業(yè)的發(fā)展進(jìn)步。因此,本文之中主要就民企員工績(jī)效考核開(kāi)展了探析,因?yàn)閅Q民宿管理公司是一家典型民企,所以,選擇其為研究對(duì)象,對(duì)其現(xiàn)階段所實(shí)施的績(jī)效考核體系現(xiàn)狀進(jìn)行了分析,并從中挖掘出了其中存在的主要問(wèn)題與不足方面,最后綜合一些理論、實(shí)踐知識(shí),設(shè)計(jì)出了針對(duì)性的改進(jìn)對(duì)策,以此來(lái)促進(jìn)其績(jī)效考核體系的發(fā)展完善,同時(shí)也給其他民企這方面的工作提供一定的啟發(fā)。關(guān)鍵詞:YQ民宿管理公司;績(jī)效考核體系;現(xiàn)狀;問(wèn)題;建議 AbstractWiththein-depthdevelopmentofhumanresourcemanagementtheoryandpractice,humanresourcemanagementhasbecomethestandardandcoreworkofmodernenterprises.Theestablishmentofenterprisesisfordevelopmentandprofit,andthecurrentmarketisincreasinglysaturated,manyindustrieshaveenteredthestockmarketcompetition,soenterprisesneedtouseinnovationtodrivedevelopment,andthekeytoinnovationanddevelopmentistalents,whichhighlightstheimportanceofperformanceappraisalmanagementsystem,whichisascientificmeansofmodernenterprisemanagement,andisconducivetostimulatetheinnovationofemployeesNewcreationanddevelopment,soastodrivetheinnovationanddevelopmentofenterprises.Atthisstage,becausethedomesticmanagementpracticeasawholelagsbehind,atthistime,althoughmanydomesticenterpriseshavecarriedouttheperformanceappraisalwork,veryfewhaveachievedtheexpectedresults,whichrestrictsthedevelopmentandprogressofdomesticenterprises.Therefore,thispapermainlyanalyzestheperformanceappraisalofemployeesinprivateenterprises.BecauseYQB&Bmanagementcompanyisatypicalprivateenterprise,itchoosesitastheresearchobjectandanalyzesthecurrentsituationofitsperformanceappraisalsystematthisstageIntheend,thepaperintegratessometheoreticalandpracticalknowledgetodesigntargetedimprovementmeasures,soastopromotethedevelopmentandimprovementofitsperformanceappraisalsystem,andalsoprovidesomeinspirationforotherprivateenterprisesinthisaspect.Keywords:YQmanagementcompany;performanceappraisalsystem;currentsituation;problems;suggestions目錄TOC\o"1-2"\h\u8408摘要 IEmployeeperformanceevaluation:afuzzyapproachImtiazAhmedandIneenSultanaAbstract:Purpose–Managersencountermanydecisionsthatrequirethesimultaneoususeofdifferenttypesofdataintheirdecision-makingprocess.Acriticaldecisionareaformanagersistheperformanceevaluationofpersonnel,whetherindividuallyorasamemberofateam.Performanceevaluationiscriticallyessentialfortheeffectivemanagementofthehumanresourceofanorganizationandevaluationofstaffthathelpdevelopindividuals,improveorganizationalperformance,andfeedintobusinessplanning.Design/methodology/approach–Performanceevaluationsrequireandofteninvolvedisparatetypesofinformationthatarevague,incomplete,objective,andsubjective.Thispaperproposesaperformanceevaluationsystemofemployeesconsideringvariousperformanceevaluationcriteriausingfuzzylogic.Themaintaskintheproposedapproachinvolvesdeterminingtheperformanceindicesofemployeesconsideringtheirrespectiveperformanceinvariousqualitativeandquantitativeevaluationcriteriaandthenselectingthebestemployeewhoholdshighestperformanceindexcomparingalltheindices.Findings–Amodelisdevelopedforanykindoforganizationwhereperformanceevaluationissignificantlyimportantforstaffmotivation,attitudeandbehaviordevelopment,communicatingandaligningindividualandorganizationalaims,andfosteringpositiverelationshipsbetweenmanagementandstaff.Fuzzycontrolisusedtodeterminetheoverallperformanceindexbycombiningresultsoftheperformanceinselectedcriteriaandprovideditinnumericalvalueswhichwillundoubtedlyensureconvenienceoftheconcernedhumanresourcepersonnelduringperformanceratingcalculation.Originality/value–Thisisthefirsttime,aperformanceevaluationmodelisdevelopedusingfuzzyapproachforanykindoforganizationwhereperformanceevaluationissignificantlyimportantforstaffmotivation,attitudeandbehaviordevelopment,communicatingandaligningindividualandorganizationalaims,andfosteringpositiverelationshipsbetweenmanagementandstaff.Keywords:Performanceevaluation;Fuzzylogic;Fuzzyset;Performanceindex;Performanceappraisal1IntroductionHumanresourceswithknowledgeandcompetenciesarethekeyassetsinassistingorganizationstosustaintheircompetitiveadvantage.Globallycompetitiveorganizationsdependontheuniquenessoftheirhumanresourcesandthesystemsformanaginghumanresourceseffectivelytogaincompetitiveadvantages.Performanceevaluationofthehumanresourcesisavitalissueinthisregard.Increatingandimplementinganappraisalsystem,managementmustdeterminewhattheperformanceappraisal(PA)systemwillbeusedforandthendecideontheprocesstoimplementthesystem.Themethodschosenandtheinstrumentsusedtoimplementthesemethodsarecrucialindeterminingwhethertheorganizationmanagesitsperformancesuccessfully.Theseappraisalmethodsarebasedonquantitativetechniqueswhichprovideapreciseoutputdefiningtheemployees’performance.However,muchoftheinformationrelatedtoPAisnotquantifiableandprecisewithcrispboundaries.Rather,thisinformationispresentedinexpressionsorwordsinnaturallanguageandwithoutprecision.Formanyorganizations,theprimarygoalofanevaluationsystemistoimproveindividualandorganizationalperformance.Soitisneedlesstosay,aproperlydesignedsystemcanhelpachieveorganizationalobjectivesandenhanceemployeeperformance.Itisutilizedtotrackindividualcontributionandperformanceagainstorganizationalgoalsandtoidentifyindividualstrengthsandopportunitiesforfutureimprovementsandassesswhetherorganizationalgoalsareachievedorservesasbasisforthecompany’sfutureplanninganddevelopment.Ithasbeenprovedbymanyresearchworksthateffectiveappraisalsystemisdirectlyrelatedtoemployeemotivationandproductivity.Itisreallydifficulttoconsidermanyfactorsatatimetoevaluateperformanceofemployeesinanorganization.Fuzzylogiccanconsidermultipleinputparameterswithuncertaintyofeachfactor.Thispaperproposesacasestudyofperformanceevaluationsystemofemployeesworkinginanorganizationbasedon20specificperformanceevaluationcriteriausingfuzzylogic.Thisresearchcallsattentiontoanalternativemethodoftheperformanceevaluationsystemasopposedtothetraditionalquantitativemethods.2LiteraturereviewThereexistsavastresearchworksinPAfieldofpersonnelmanagement.Manyquantitativeandjudgmentalmethodsevolveduringthepastyears.However,thispapertriestocoversomeoftheinsightsfromthosecontributions.Theimportanceofperformanceevaluationofpersonnelanditsrelationshiptothefirm’sperformanceiswelldocumentedintheliterature(Lowe,1986;KatzenbachandSmith,1993;Kilduffetal.,2000;Higgs,2005).Avarietyofappraisaltechniquesareavailabletomeasureperformance(ChangandHahn,2006;Jiangetal.,2001;Armentrout,1986;ArveyandMurphy,1998;SanchezandDeLaTorre,1996;Stronge,1991).Bretzetal.(1992)reviewedthePAliteraturepublishedinbothacademicandpractitioneroutletsbetween1985and1990,brieflydiscussedthecurrentstateofPApractice,highlightthejuxtapositionofresearchandpractice,andsuggesteddirectionsforfurtherresearch.Kleinetal.(1993)proposedamodelforPAinterviewadaptedfromopensystemstheory.Ying-FengandLing-Show(2002)conductedastudyformeasuringperformancesoflecturersworkinginuniversitiesofTaiwanbyemployingfuzzysyntheticdecisionapproach;theprocedureofmeasuringperformancesoflecturersismadethroughpointsgiventocriteriawithspecificlevelofsignificanceandvaryingbetween1and5invalue.AsreformisacommonthemeinAmericanpublicadministration,KelloughandSally(2003)examinedtheextenttowhichthesekindsofpersonnelreformshavebeenimplementedbystategovernments.Areformindexisdevelopedtodocumenttheconsiderablevariationamongthestatesintheirapproachtopersonnelpractices.Kciuk(2007)presentedpersonnelmanagementdevelopmentinrecentyears.Themainfocuswasontheworkersselectionfollowsthroughthechoiceofthesuitablemethodsofrecruitmentandselectionprecededtheplanningofpersonnelneeds.Itisveryclearlyandwellunderstoodfromhispaperthattheworkerschoiceisthecontinuousprocess,adaptedtothechangingneedsoftheorganization.Law(2007)illustratedhowperformanceappraisalsarearelicofexternal-controlbossmanagementandexplainswhythePAprocessisgenerallydislikedbyboththeappraiserandtheemployeebeingappraised.Thegoalsandunderlyingassumptionsheldbymanagersandhumanresourcespersonnelarediscussed,andsomeofthecounterproductiveaspectsofperformanceappraisalsareidentified.Finally,alternativestoperformanceappraisalsareexplored,focussingonworkplacerelationshipsandcommunication.AliandOpatha(2008)investigatedtherelationofPAtobusinessperformanceinSriLankanapparelfirms;tofindoutwhetherasignificantdifferenceexistsbetweenlargeapparelfirmsandnon-largeapparelfirmswithregardtoperceivedqualityofPAandtorevealwhetherasignificantdifferenceexistsbetweenlargeapparelfirmsandnon-largeapparelfirmswithregardtobusinessperformance.Threehypotheseswereformulatedusingdeductiveapproach.However,thestudyrevealednostatisticalevidencetoclaimthatthedegreeofperceivedqualityofPAoflargeapparelfirmsissignificantlydifferentfromthatofnon-largeapparelfirmsandthattheperceiveddegreeofbusinessperformanceoflargeapparelfirmsissignificantlydifferentfromthatofnon-largeapparelfirms.Jafarietal.(2009)proposedaframeworkfortheselectionofappraisalmethodsandcomparesomePAmethodsinordertofacilitatetheselectionprocessfororganizations.Thevalueofthisframeworkisthat,withuseofit,organizationscanevaluatetheirPAmethodwithrespecttothekeyfeaturesofitbeforeimplementinganymethodaswellasexpendingextracosts.Rasheedetal.(2011)exploredvariousaspectsofPAsystemsusedforteachersinhighereducationalinstitutions.ResearchershaveundertakenPublicSectorUniversityofPakistan,asacasestudyinthepresentresearch.AcombinationofqualitativeandquantitativeresearchapproachhasbeenadoptedwhichconsistofaquestionnaireinordertogetprimarydataforinvestigatingdifferentaspectsofcurrentPAsystemandin-depthinterviewsinordertostudythoroughperceptionsofteachersregardingPAapproachesintheirinstitution.Findingshaveshownthatobsoleteevaluationsystem,exclusionofstudents’feedback,untrainedevaluators,anddecreasedmotivationfortheprocessarethepotentialhinderingfactorsforPAsystemsofthecasestudyuniversity.Ochotietal.(2012)investigatedthemultifacetedfactorsinfluencingemployeePAsystemintheMinistryofStateforProvincialAdministration,NyamiraDistrict,Kenya.MultipleregressionanalysistechniquewasusedtoexplainthenatureoftherelationshipbetweenPAsandthefactorsthatinfluenceit.Daonis(2012)examinedthestatusofthePAsystemofNassConstructionCompanyanditsimplicationtoemployees’performance.Therespondentsofthisstudyweretenuredemployees.TheresultofthestudyshowedthatthePAsystemofthecompanyareinplace,alignedwiththevisionandmissionoftheinstitution,andisaccurateintermsofcontentandpurpose.Ontheotherhand,theresultsreflectedthatthePAsystemofthecompanyhasbroughtaboutbothpositiveandnegativeimpactontheemployeesperformance.ToppoandPrusty(2012)focussedtostudytheevolutionofemployee’sPAsystem,criticsthesystemsuffered,andhowtheperformancemanagementsystemcametothepractice.Theydifferentiatedthesetwosystems,employee’sPAandmanagementsystem.PerformancemanagementeliminatestheshortcomingsofPAsystemtothesomeextent.S??rb(2012)developedatoolbasedonfuzzylogicforselectionofhumanresourcesincompanies,generallyandofthoseoftop-managementwithinminingprojectfromRos?iaMontana?,inparticular.Theproposedmethodologyisamultidisciplinaryone,addressingissuesfromareassuchasmanagement,mathematicsorpsychology.ItsdesignprojectedinthispaperinapersonalmannerallowsselectingthemostsuitablemanagerofprocessingplantofpreciousmetalswithinminingprojectfromRos?iaMontana?,akeypostforthesuccessofthisproject,whichrequiresemployingthemostappropriatespecialist,takingintoaccountthesubjectivityofassessingtheweightofimportanceofsomeselectioncriteriaandofassessingthedegreeinwhichthepotentialcandidatessatisfytherequirementsofthesecriteria,alltheseaspectsmodeledunderthespectrumoffuzzylogic.ChattopadhayayandGhosh(2012)pointedoutsomeseriouslimitationsofforceddistributionsystemandproposeasimplemodificationtoovercometheselimitations.Extensivesimulationstudiesshowthatthemodifiedalgorithmisuniformlybetterthantheexistingoneoverdifferentschemesforallocationsofemployeestodifferentprojects.Manyorganizationsdonotusethesystematicwaytoevaluatetheperformanceoftheiremployeesthatoftenmakestheirevaluationmethodvagueandinefficient.Soitisverynecessarytodevelopasystematicapproachforregularusetoperformtheperformanceevaluationprocessatplanningstage.Againorganizationsuseseveralcriteriaforevaluatinganemployeewhichmakesthewholeprocessverycomplexastherearedifferentrulesforeachcriterionwithdifferentpriority.Soobtainingatotalperformanceindexforanemployeeconsideringallcriteriaisatiresomeprocess.Fuzzyrule-baseddecisionmakingcouldsolvethisproblemeasilyasfuzzylogictakesintoaccountvariouscriteriaandprovidesaneasierwaytoperformtheaggregatedcalculationbasedongivenruleswhichiscomplextodoinusualtraditionalmethod.Soformulatingamodelwhereemployees’performancesareratedinsomedefinedfactorsaccordingtojudgmentscaleandusingthisratedperformanceasinput,fuzzylogiccouldbeappliedtodeterminetheoverallperformanceindexofanemployee.Fuzzylogichelpstofindtheperformanceindexofanindividualifthecompany’sperformancedataandratingbasedonjudgmentareavailable.Inthismodel,thejudgmentoftheperformanceonascaledecidedbyevaluatorandestablishmentofrulesinfuzzylogicaccordingtowhichthecalculationworksarethemostimportanttasks.Inthefuzzyenvironmentnumerousstudieshavebeenconductedindifferentareasandapplications.Yehetal.(2000)developedaneffectivefuzzymulticriteriaanalysisapproachtoevaluateperformanceofurbanpublictransportsystemsthatinvolvesmultiplecriteriaofmulti-levelhierarchiesandsubjectiveassessmentsofdecisionalternatives.AcasestudyontenbuscompaniesofanurbanpublictransportsysteminTaiwanisconductedtoillustratetheeffectivenessoftheapproach.GalinecandVidovic(2006)arguedthatprojectteamworkdependsconsiderablyonthecontributionofitsmembersanditsmanagementaswell.Toidentifytheimportanceofeachindividual,aleader/managermustevaluateindividualcontributions.Aleaderusuallyhasdefectiveandincompleteinformationathisdisposaland,besides,issubjective.Tosolvetheaforesaidproblem,fuzzyapproachandfuzzylogicareused.Fuzzyevaluationsystemhasbeendesignedtoreduceevaluationsubjectivity.BeheshtiandLollar(2008)developedafuzzylogicmodelapproachtodecisionmakinganditsvalueformanagersbyillustratingitsapplicationtoemployeeperformanceappraisals.PakdamarandGuler(2008)developedafuzzylogicapproachintheperformanceevaluationofreinforcedconcretestructures.Theyshowedthattheperformancelevelcanbedefinedtobeflexiblebyusingcertainweightedvaluesdependingonnumberanddeformationlevelofelements.Paladini(2009)usedfuzzylogictostructureanevaluationprocessoftheperformancelevelsofhumanresourceswhooperateinbothindustrialandserviceprovidingorganizations.Amodelhasbeendevelopedtoeachsector.Theperformancestandardsreflectanidealprofileofdecision-makingagentsinindustrialandserviceprovidingorganizations.Wuaetal.(2009)proposedaFuzzyMultipleCriteriaDecisionMakingapproachforbankingperformanceevaluation.Theysummarizedtheevaluationindexessynthesizedfromtheliteraturerelatingtobankingperformance.Then23indexesfitforbankingperformanceevaluationwereselectedthroughexpertquestionnaires.Furthermore,therelativeweightsofthechosenevaluationindexeswerecalculatedbyFAHP.AfterthatMCDManalyticaltoolsofSAW,TOPSIS,andVIKORwere,respectively,adoptedtorankthebankingperformanceandimprovethegapswiththreebanksasanempiricalexample.Tuzkayaetal.(2009)developedahybridfuzzyanalyticnetworkprocessandfuzzypreferencerankingorganizationmethodfortheevaluationofsuppliers’environmentalperformancesandprovidedanumericalexampleforbetterunderstandingwithasensitivityanalyses.YeeandChen(2009)proposedaPAsystemusingmultifactorialevaluationmodelindealingwithappraisalgradesanditisforevaluatingstaffperformancebasedonspecificPAcriteria.PaulandAzeem(2010a)proposedamodelfortheselectionofoptimalshiftnumbersconsideringinventoryinformation,customerrequirements,andmachinereliabilityusingfuzzylogic.Themaintaskinvolvesoptimizingtheshiftperiodsconsideringconstraintsofrawmaterial,duedate,demand,andfinishedgoodsinventoryandmachinebreakdown.Amodelisdevelopedforanykindofmanufacturingcompanywhereshiftperiodsaffectcompany’sprofitandcost.Fuzzycontrolisusedtooptimizethenumberofshiftsundertheconstraintsofinputvariables.PaulandAzeem(2010b)usedfuzzysetsandlogictotackleuncertaintiesinherentinactualflowshopschedulingproblemstominimizework-in-processinventory.Fuzzyduedates,costovertimeandprofitrateresultthejobpriorityandtodeterminethemachinepriorityprocessingtimeofeachmachineisconsidered.MATLABFuzzyToolboxisusedtocalculatetheprioritiesofjobsandmachinesatdifferentstages.Finally,jobsareassignedintomachinesbasedonagroupingandsequencingalgorithmthatminimizesthetotalworkinprocessinventory.Sun(2010)developedaperformanceevaluationmodelbasedontheFAHPandthetechniquefororderperformancebysimilaritytoidealsolution,fuzzyTOPSISwherethevaguenessandsubjectivityarehandledwithlinguisticvaluesparameterizedbytriangularfuzzynumbers.Zemkova′(2011)usedfuzzysetsinperformanceevaluationofemployeesinacompanywheremultiplecriteriaevaluationisutilized.Chengetal.(2011)developedanevolutionaryfuzzyhybridneuralnetworktoenhancetheeffectivenessofassessingsubcontractorperformanceintheconstructionindustry.YadavandSingh(2011)proposedafuzzyexpertsystemforstudentacademicperformanceevaluationbasedonfuzzylogictechniques.Manoharanetal.(2011)demonstratedhowanintegratedtoollikefuzzymultiattributedecisionmaking,withFAHP,fuzzyqualityfunctiondeploymentisappliedasafairevaluatingandsortingtooltosupportthePAsystem.Severalapproachesusingfuzzylogictechniqueshavebeenproposedforevaluatingstudentacademicperformanceandcomparetheresultswithexistingstatisticalmethod.Sahuetal.(2012)proposedanefficientsupplierappraisementsystembyconsideringgreenperformancecriteria,infuzzyenvironment.Afuzzyevaluationindexhasbeenestimatedtowardassessingsuppliers’greenperformanceextent.Meenakshi(2012)proposedamultisourcefeedback-basedPAsystemusingfuzzylogicdecisionsupportsystem.YarahmadiandSadoughi(2012)presentedacomprehensiveapproachfordecisionmakerstoevaluateandprioritizeenvironmentalindicesusingaTOPSIS.3MethodologyThemodelproposedinthisresearchutilizesfuzzyinferencesystem(FIS)whichisanoptimizationtechniquethatconsidersdifferentinputsandrelatesthoseinputswithoutputwithsomerules.Rulesindicatetherelationshipbetweeninputsandoutputs.Theoutputisoptimizedbasedonrelationshipbetweenvariables.Thefinaloutputisobtainedfromtheaggregatedoptimizedresultofindividualrule.FuzzysettheorywasoriginallypresentedbyZadeh(1965)inhisseminalpaper“FuzzySets”inInformationandControl.Fuzzylogicwasdevelopedlaterfromfuzzysettheoryprimarytoreasonwithuncertainandvagueinformationandsecondarytorepresentknowledgeinoperationallypowerfulform(FranttiandMahonen,2001).Fuzzyinferenceistheprocessofformulatingthemappingfromagiveninputtoanoutputusingfuzzylogic.Themappingthenprovidesabasisfromwhichdecisionscanbemade,orpatternsdiscerned.TherearetwotypesofFISsthatcanbeimplementedinFuzzyLogicToolbox:Mamdani-typeandSugeno-type.Thesetwotypesofinferencesystemsvarysomewhatinthewayoutputsaredetermined.Becauseofitsmultidisciplinarynature,FISsareassociatedwithanumberofnames,suchasfuzzy-rule-basedsystems,fuzzyexpertsystems,fuzzymodeling,fuzzyassociativememory,fuzzylogiccontrollers,andsimply(andambiguously)fuzzysystems.Mamdani’sfuzzyinferencemethodisthemostcommonlyseenfuzzymethodology.Mamdani’smethodwasamongthefirstcontrolsystemsbuiltusingfuzzysettheory.ItwasproposedbyMamdaniandAssilian(1975)asanattempttocontrolasteamengineandboilercombinationbysynthesizingasetoflinguisticcontrolrulesobtainedfromexperiencedhumanoperators.Mamdani-typeinference,asdefinedforFuzzyLogicToolbox,expectstheoutputmembershipfunctionstobefuzzysets.Aftertheaggregationprocess,thereisafuzzysetforeachoutputvariablethatneedsdefuzzification.Itispossible,andinmanycasesmuchmoreefficient,touseasinglespikeastheoutputmembershipfunctionsratherthanadistributedfuzzyset.Thistypeofoutputissometimesknownasasingletonoutputmembershipfunction,anditcanbethoughtofasapre-defuzzifiedfuzzyset.ItenhancestheefficiencyofthedefuzzificationprocessbecauseitgreatlysimplifiesthecomputationrequiredbythemoregeneralMamdanimethod,whichfindsthecentroidofatwo-dimensionalfunction.Ratherthanintegratingacrossthetwo-dimensionalfunctiontofindthecentroid,theweightedaverageofafewdatapointsisused.Sugeno-typesystemssupportthistypeofmodel.Ingeneral,Sugeno-typesystemscanbeusedtomodelanyinferencesysteminwhichtheoutputmembershipfunctionsareeitherlinearorconstant.Nova′ketal.(1999)discussedthemathematicalprinciplesoffuzzylogicintheirbook.Accordingtothis,mathematicalprinciplesoffuzzylogicprovideasystematicstudyoftheformaltheoryoffuzzylogic.Thisbookpresentsfuzzylogicasthemathematicaltheoryofvaguenessaswellasthetheoryofcommonsensehumanreasoning,basedontheuseofnaturallanguage,thedistinguishingfeatureofwhichisthevaguenessofitssemantics.InFuzzyLogicToolbox,therearefivepartsofthefuzzyinferenceprocess:fuzzificationoftheinputvariables,applicationofthefuzzyoperator(ANDorOR)intheantecedent,implicationfromtheantecedenttotheconsequent,aggregationoftheconsequentsacrosstherules,anddefuzzification.Thesesometimescrypticandoddnameshaveveryspecificmeaningthatisdefinedinthefollowingsteps.StepI:fuzzificationofinputsThefirststepistotaketheinputsanddeterminethedegreetowhichtheybelongtoeachoftheappropriatefuzzysetsviamembershipfunctions.InFuzzyLogicToolbox,theinputisalwaysacrispnumericalvaluelimitedtotheuniverseofdiscourseoftheinputvariableandtheoutputisafuzzydegreeofmembershipinthequalifyinglinguisticset.Fuzzificationoftheinputamountstoeitheratablelookuporafunctionevaluation.Eachinputisfuzzifiedoverallthequalifyingmembershipfunctionsrequiredbytherules.StepII:applicationoffuzzyoperatorAftertheinputsarefuzzified,thedegreetowhicheachpartoftheantecedentissatisfiedforeachruleisknown.Iftheantecedentofagivenrulehasmorethanonepart,thefuzzyoperatorisappliedtoobtainonenumberthatrepresentstheresultoftheantecedentforthatrule.Thisnumberisthenappliedtotheoutputfunction.Theinputtothefuzzyoperatoristwoormoremembershipvaluesfromfuzzifiedinputvariables.Theoutputisasingletruthvalue.Anynumberofwell-definedmethodscanfillinfortheANDoperationortheORoperation.InFuzzyLogicToolbox,twobuilt-inANDmethodsaresupported:min(minimum)andprod(product).Twobuilt-inORmethodsarealsosupported:max(maximum),andprobor(probabilisticOR)method.StepIII:implicationmethodBeforeapplyingtheimplicationmethod,therule’sweightisdetermined.Everyrulehasaweightbetween0and1,whichisappliedtothenumbergivenbytheantecedent.Generally,thisweightis1andthushasnoeffectatallontheimplicationprocess.Fromtimetotimeyoumaywanttoweightonerulerelativetotheothersbychangingitsweightvaluetosomethingotherthan1.Afterproperweightinghasbeenassignedtoeachrule,theimplicationmethodisimplemented.Aconsequentisafuzzysetrepresentedbyamembershipfunction,whichweightsappropriatelythelinguisticcharacteristicsthatareattributedtoit.Theconsequentisreshapedusingafunctionassociatedwiththeantecedent(asinglenumber).Theinputfortheimplicationprocessisasinglenumbergivenbytheantecedent,andtheoutputisafuzzyset.Implicationisimplementedforeachrule.Twobuilt-inmethodsaresupported,andtheyarethesamefunctionsthatareusedbytheANDmethod:min(minimum),whichtruncatestheoutputfuzzysetandprod(product),whichscalestheoutputfuzzyset.StepIV:aggregationofalloutputsBecausedecisionsarebasedonthetestingofalloftherulesinaFIS,therulesmustbecombinedinsomemannerinordertomakeadecision.Aggregationistheprocessbywhichthefuzzysetsthatrepresenttheoutputsofeach
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