Fuzzy Analytical Hierarchy Process Method to Determine the ...

Fuzzy Analytic Hierarchy Process is a method of Analytic Hierarchy Process (AHP) developed with fuzzy logic theory. Fuzzy AHP method is used similar to the ... AdvancesinFuzzySystems/2018/Article/OnthispageAbstractIntroductionDataAvailabilityMaterialsandMethodsDiscussionConclusionConflictsofInterestReferencesCopyrightRelatedArticlesSpecialIssueApplicationsofFuzzyMulticriteriaDecisionMakingtoComplexEngineeringProblemsViewthisSpecialIssueResearchArticle|OpenAccessVolume2018|ArticleID9094380|https://doi.org/10.1155/2018/9094380ShowcitationFuzzyAnalyticalHierarchyProcessMethodtoDeterminetheQualityofGemstonesMochammadSobandiDwiPutra,1SeptiAndryana,1Fauziah,1andArisGunaryati1ShowmoreGuestEditor:QiZengReceived25May2018Accepted13Sept2018Published01Oct2018Theselectionofqualitygemstonesrequiresaspecialabilitytoselectandassessthequalityofgemstonestobetraded.Thediversityoftypesofgemstonesandconsumersbecomesanobstacleinitselfwhentheknowledgeandabilityofindividualstoanalyzethequalityofgemstonesisminimal.Thedecision-makingmethodusedisFuzzyAnalyticalHierarchyProcess(F-AHP)methodwhichiswidelyusedinvarioussectors.F-AHPiseasytoadapttomanydecisionissues;theresearchproposesadecision-makingsystemusingtheF-AHPalgorithmtoanalyzethequalityofgemstones.TheresultsobtainedwiththeuseofF-AHPmodelintheselectionofqualitygemstonesshowthehighestqualityofgemstonesofallstonescompared,Rubi1,withaweightvalueof0.152942.1.IntroductionManytimes,wearealwaysfacedwithseveraloptionsfortherightdecision-making.Itisdifficulttodetermineanaccuratechoiceaccordingtopredeterminedcriteria.Decision-makingissuesarealsoexperiencedwhenselectingqualitygemstones.Forthegemstonesentrepreneur,specialskillsarerequiredtoselectorassessthequalityofgemstonestobetraded.Thediversityoftypesofgemstonesandconsumertypesinchoosinggemstonesiscertainlyaconstraintwhenthedataisincompleteandthereisalackofindividualknowledgeaboutanalyzingthequalityofgemstones.Tomaintaintheconsistencyofproductqualityandinaccordancewiththedemandsofthemarket,itisnecessarytohavequalitycontroloneligibleproducts,sothattheerrordoesnothappenagain.Thesystemtobecreatedisasolutionthatcanassistdecision-makingfordecision-makersinassessingandselectingqualitygemstonesaccuratelyandeffectively.Inpreviousresearch,severalstudiesusingtheF-AHPmethodhavebeenprovenfromseveralpreviousstudieswiththeconclusionthattheF-AHPmethodcanbeappliedandeffectiveformanyproblemsinreallife.Chien-ChangChouandKer-WeiYu[1]proposeahybridfuzzyAHPtodealwiththedecision-makingproblemsinanuncertainandmultiple-criteriaenvironmentchoice.TheF-AHPadoptedbytheresearch[2],whichcombinestheAHPwithfuzzysettheory,cannotonlycapturethethinkinglogicofhumanbeingsbutalsofocusontherelativeimportanceoftheevaluationcriteria.Injournal[3],theresultobtainedshowsthebestbalanceofperformanceforcriteriafromdifferentcategoriessuchasphysicochemicalpropertiesaswellassafety,environmental,andhealthaspects.TheassumptionmadeinF-AHPapproachisthatallthecriteriainvolvedareindependentofeachother.However,inpracticetherelationshipamongcriteriaisusuallycomplex,andtheremightbeinterdependencies.Tocontrolthequality,weneedarelevantelementandmethod[4];fuzzymodelcanbeusedwithvariousmcdmmethods[5].F-AHPmodelisagoodreferralfordecision-makers[6].ThefuzzyAHPmethodisapplicableasacontrolforthequalityandisusefulformulticriteriadecision-makingproblems[7].Thecriteriapeoplethinkofarethesizethatmakesthequalityofthegemstonebetterbutwithothercriteriaasacomparisoncanmakethequalityofsmallerstonesbetterthanlargerones[8].ByusingF-AHPmethodwecanhelpadecision-makertomakemoreefficient,flexible,andrealisticdecisionsbasedupontheavailablecriteriaandalternatives[9].Therefore,theauthorswishtoapplytheF-AHPmethodtodeterminethequalityofgemstones.2.DataAvailabilityThedataandcriteriainTable1werecollectedbyconsultingthedirectorofKantorPromosiBatuMuliaIndonesia.ThedatacanbeseenfromthestonecertificateissuedbyKantorPromosiBatuMuliaIndonesia.Everytimewebuygemstoneswewillgetcertificateofauthenticityofstone;inthecertificatetherearecriteriaofstone.Table1 Dataofgemstonescontainingspecificgravity,color,hardness,cutting,andclarityasthemaincriteria.Thedatacanbeseenfromthegemstonecertificate.3.MaterialsandMethodsAnalyticHierarchyProcess(AHP)isadecisionsupportmethoddevelopedtocompleteproblembybreakingthesolutionproblems,groupingthem,andthenarrangingthemintoahierarchicalstructure.Toobtainprioritycriteria,thismethodusesacomparisonofcriteriapairedwithameasurementscalethathasbeendetermined.ThemaininputoftheAHPmethodistheperceptionofexpertsorexperts,sothereisafactorofsubjectivityinretrievaldecision.Thismethodalsotakesintoaccountdatavaliditywithinconsistencylimits[10].However,considerableuncertaintyanddoubtingivinganassessmentwillhaveanimpactontheaccuracyofthedataandtheresultsobtained.Basedonthis,furthertheorywasdeveloped,namely,themethodofFuzzyAnalyticHierarchyProcess.FuzzyAnalyticHierarchyProcessisamethodofAnalyticHierarchyProcess(AHP)developedwithfuzzylogictheory.FuzzyAHPmethodisusedsimilartothemethodofAHP.ItisjustthattheFuzzyAHPmethodsetstheAHPscaleintothefuzzytrianglescaletobeaccessedpriority.Inthissection,theF-AHPmethodwasdeveloped.Theprocedureusedintheproposedmethodisdescribedasfollows.Step1(definetheproblemanddeterminethedesiredsolution(seeFigure1)).Weneedtodefinetheproblemaccordingtothecriteriausedtodeterminethegemstonesofquality.Specificgravity,color,hardness,cutting,andclarityareusedasthemaincriteriafordetermininggemstonequality.Thisissomedatafromthegemstonecertificate(seeTable1).Figure1 BlockdiagramhassixstepsofF-AHPphaseprocess.Theweightofthestonehasaunitofcarat(ct);thegreatertheweightofagemstone,thegreateritssize.StonehardnessunitiscalledMohsbecausethenameofthefirstpersontodoresearchonthehardnessofagemstonewasFriedrichMohs,ageologistandmineralogistfromGermanyin1812.TheclaritylevelofagemstoneisdividedintoIF,VVS1,VVS2,VS1,VS2,I1,I2,etc.Thegemstonecolorlevelisseenfromthelevelofclarityofcolorseenbytheeye,giventhelevelsofB,A,AA,AAA,andsoon.Thelevelofcuttingqualityisseenfromitsproportionalandsymmetricalshapeofgemstonespieces.Step2(createacomparisonmatrix(seeFigure1)).AfterweknowthedataandcriteriastoneinTable1weneedtocreateacomparisonmatrix.Thematrixusedissimple,hasastrongpositionfortheconsistencyframework,obtainsotherinformationthatmayberequiredwithallpossiblecomparisons,andisabletoanalyzetheoverallprioritysensitivityforchangesinconsideration.Herearetheequationsusedtodefinepairwisecomparisons:wherendenotesthenumberofcriteriacompared,areweightsfortheicriterion,andistheratiooftheweightoftheicriterionandj.AfterknowingthecomparisonofitscriteriainTable2,thenextthingdoneistonormalizeeachcolumnintothematrixformbydividingeachvalueinthecolumniandrowjwiththelargestvalueincolumni.ThentheresultsofthematrixnormalizationfromTable2areobtainedasfollows:Table2 Comparisonofcriteria,astheweightedvalueofeachcriterion.Step3(checkingforconsistency(seeFigure1)).Thecomparisonoftheconsistencyindexwitharandomgenerator(RI)valueislistedinTable3setbySaaty[10].Thisvaluedependsonthematrixordern.Table3 Ratioindex.Consistencyisexpectedtobenearperfecttoproduceadecisionthatisclosetovalid.Hereistheequationusedtocalculatethevalueofconsistency.Firstwemustrecognizethevalueoftheeigenvectorwhichistheweightedvalueofthecriterion.Tocalculatetheeigenvector,weusethefollowingequation:istheeigenvector,whereisthesumofthematrixnormalizationvaluesandisdividedbythenumberofcriterionThelargesteigenvalueisthenumberoftimesmultiplyingthenumberofcolumnswiththemaineigenvector(seeTable4).SoitcanbeobtainedbytheequationAfterobtainingmaximumlambdavalue,thevalueofCIcanbedetermined.whereCIistheconsistencyindexandmaximumlambdaisthelargesteigenvalueofthen-ordermatrix.IfthevalueofCIiszero(0),thismeansthematrixisconsistent.IfthevalueofCIobtainedisgreaterthan0(CI>0),thenthelimitofinconsistencyappliedbySaatyistested.TestingismeasuredusingConsistencyRatio(CR),i.e.,indexvalue(Table3),orcomparisonbetweenCIandRI.TheRIvalueusedisinaccordancewiththeordernmatrix.IftheCRofasmallermatrixis10%(0,1),thismeansthattheinconsistencyofeachopinionisconsideredacceptable.Theconsistencyvalueof0.1058isequivalentto10%inconsistency;thisvaluecanstillbetoleratedbecausetheconsistencyvalueindexmustbelessthan0.1.Table4 Eigenvectoroncriteria.Step4(setupTriangularFuzzyNumber(TFN)(seeFigure1)).TheF-AHPscalehasthreevalues,namely,thelowestvalue(lower,L),middlevalue(median,M),andhighestvalue(upper,U).Soeachfuzzysetwillbedividedinto2(seeFigure2),exceptforthesamecomparisonset,orcanbeseenontheTFNscale(seeTable5).Table5 TFNscale.Figure2 GraphofFuzzyTriangleSet.Basedontheindex(seeTable5),thecomparisonvalueinTable2willbemadeintoaTFNset(seeTable6).Table6 TFNsetofcriteria;eachvalueinthecriteriacomparison(seeTable2)ischangedtoTFNreferringtotheTFNscale.Step5(calculatetheweightvalueofthefuzzyvector(seeFigure1)).AftertheAHPcomparisonvalueistransformedtoF-AHPscalevalue,fuzzysynthesisvalueiscalculated.Theprocesstogetfuzzysynthesisvalueisshownusingequationofthefollowingformula:Information:=fuzzysynthesisvalue=summingthecellvalueinthatcolumnstartingfromcolumn1ineachrowmatrixi=rowj=columnAfterthecomparisonoffuzzysynthesisvalues(seeTable7),wewillgetthedefuzzificationordinatevalue.Fromtheabovecalculation,wecancalculatethevaluesofvand.Tocalculateweusetheequationofthefollowingformula.Calculatingthevalueofthefuzzyvectorweight(),calculationofthefuzzyweightvalueisshownusingtheequationofthefollowingformulacollectingordinatevaluesthathavebeenpreviouslyobtained,asbelow.Normalizationofvectorweightvaluesisobtainedbytheequationofthefollowingformula,Table7 Synthesisvalue.Step6(rankingandselectionofdecisions(seeFigure1)).Nextistodoanalternativevaluecalculationwherethealternativesettlementmeasuresarethesameasthecompletionstepsonthecriteria.Eachalternativeelement’sweightvalue(seeTable8)willbecalculatedbytheweightofthecriteriaelementandwillbedirectedtogetthedecisionresult.Table8 Criteriaweightvalue,theresultofcalculationwhichcontainstheweightvalueofeachcriterion.4.ResultandDiscussionThebuiltsystemconsistsofseveralmenusthatarethestagesinrunningthedecisionsupportsystem.Thefirstthingtodoisloginfirst.Tobeabletousethissystemweneedtologin.Afterlogin,wewillenterintothemainmenu.OnthemainpagetheF-AHPalgorithmandanydataneededtostartthesystemprocessareexplained.Afterthatalternativedataandcriteriaareenteredintothesystem.Thegemstonedatawehaveneedtobeinputintothealternatedatainputpageaccordingtothecriteriaalongwiththecriteriadataweinputintotheinputdatapagecriteria.Thenextthingtodoistoprovideacomparisonofthecriteriaandthevalueofalternativecomparisontoeachcriterion.Afterallhasbeendone,nextwecandothefollowingprocess.IntheprocesspagewecanseethevalueofcriteriacomparisonandTFNsetofcriteria.Whentheprocessiscompleted,thiswillresultintherankingofeachalternative;thedecision-makercandeterminewhichgemstonesarequalifiedfromthegemstonesbeingcompared.FromtherankingresultsinFigure3andTable9,itcanbeconcludedthatalternative1hasthemostoptimumweightvaluecomparedwithotheralternatives.Therefore,adecisioncanbemadethatRubi1isthehighest-qualitygemstoneofallstonescompared.Table9 Valueofalternativecalculationresultoncriteria.Figure3 Rankinggraph:rankingisderivedfromtheresultofalternateweightmatrixbyweightofcriterion.5.ConclusionTheconclusionofthisresearchisasfollows:wecreatedasystemthatcanassistdecision-makinginassessingandchoosingqualitygemstonesaccuratelyandeffectivelybyusingF-AHPalgorithm.Thefocusonthedecisionofthesystemismoreonthedecisionofstonesbasedonthesametypeofstonename;thisisbecause,forthedecisionsystemtobemoreappropriateandrelevantforuseasaconsiderationindecision-making,itisimpossibletocompareonestonewithstonesofdifferenttypes,notinthesameclassquality,sotheendresultofthesystemisbasedontheclassificationofthetypeofstonename.AsshowninFigure3weobtainedtheresultbyusingtheF-AHPmodelintheselectionofqualitygemstonesRubi1withaweightvalueof0.152942,Rubi2of0.075731,Ruby3of0.050075,andRuby4andRubi5of0.ThisweightingvalueindicatesthatagemstoneofthehighestqualityisRubi1withaweightvalueof0.152942ofallstonescompared.DataAvailabilityThedatausedtosupportthefindingsofthisstudyareavailablefromthecorrespondingauthoruponrequest.ConflictsofInterestTheauthorsdeclarethattheyhavenoconflictsofinterest.ReferencesChien-ChangChouandKer-WeiYu,“ApplicationofaNewHybridFuzzyAHPModeltotheLocationChoice,”MathematicalProblemsinEngineering,vol.2013,ArticleID592138,12pages,2013.Viewat:PublisherSite|GoogleScholar|MathSciNetH.-Y.Wu,G.-H.Tzeng,andY.-H.Chen,“AfuzzyMCDMapproachforevaluatingbankingperformancebasedonBalancedScorecard,”ExpertSystemswithApplications,vol.36,no.6,pp.10135–10147,2009.Viewat:PublisherSite|GoogleScholarJ.Ooi,M.A.B.Promentilla,R.R.Tan,D.K.S.Ng,andN.G.Chemmangattuvalappil,“IntegrationofFuzzyAnalyticHierarchyProcessintomulti-objectiveComputerAidedMolecularDesign,”Computers&ChemicalEngineering,vol.109,pp.191–202,2018.Viewat:PublisherSite|GoogleScholarJ.-C.TuandC.-L.Hu,“ApplyingtheFuzzyAnalyticHierarchyProcesstoConstructtheProductInnovativeServiceSystemofWeddingPhotographyApparel,”MathematicalProblemsinEngineering,vol.2015,2015.Viewat:GoogleScholarM.Shaverdi,“ApplicationofFuzzyAHPApproachforFinancialPerformanceEvaluationofIranianPetrochemicalSector,”ProcediaComputerScience,pp.995–1004.Viewat:GoogleScholarR.-H.Chiu,L.-H.Lin,andS.-C.Ting,“Evaluationofgreenportfactorsandperformance:afuzzyAHPanalysis,”MathematicalProblemsinEngineering,vol.2014,ArticleID802976,12pages,2014.Viewat:PublisherSite|GoogleScholarL.Wang,J.Chu,andJ.Wu,“Selectionofoptimummaintenancestrategiesbasedonafuzzyanalytichierarchyprocess,”InternationalJournalofProductionEconomics,vol.107,no.1,pp.151–163,2007.Viewat:PublisherSite|GoogleScholarS.-H.Tsaura,T.-Y.Chang,andC.-H.Yen,“TheevaluationofairlineservicequalitybyfuzzyMCDM,”TourismManagement,vol.23,no.2,pp.107–115,2002.Viewat:PublisherSite|GoogleScholar.Kaur,“SelectionofVendorBasedonIntuitionisticFuzzyAnalyticalHierarchyProcess,”AdvancesinOperationsResearch,vol.2014,ArticleID987690,10pages,2014.Viewat:PublisherSite|GoogleScholar|MathSciNetT.L.SaatyandK.P.Kearns,AnalyticalPlanningTheOrganizationofSystems,PergamonPress,1985.CopyrightCopyright©2018MochammadSobandiDwiPutraetal.ThisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.PDFDownloadCitationDownloadotherformatsOrderprintedcopiesViews24566Downloads4637Citations