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Int.J.ServicesSciences,Vol.1,No.1,200883Copyright©2008InderscienceEnterprisesLtd.DecisionmakingwiththeanalytichierarchyprocessThomasL.SaatyKatzGraduateSchoolofBusiness,UniversityofPittsburgh,Pittsburgh,PA15260,USAE-mail:saaty@katz.pitt.eduAbstract:Decisionsinvolvemanyintangiblesthatneedtobetradedoff.Todothat,theyhavetobemeasuredalongsidetangibleswhosemeasurementsmustalsobeevaluatedasto,howwell,theyservetheobjectivesofthedecisionmaker.TheAnalyticHierarchyProcess(AHP)isatheoryofmeasurementthroughpairwisecomparisonsandreliesonthejudgementsofexpertstoderivepriorityscales.Itisthesescalesthatmeasureintangiblesinrelativeterms.Thecomparisonsaremadeusingascaleofabsolutejudgementsthatrepresents,howmuchmore,oneelementdominatesanotherwithrespecttoagivenattribute.Thejudgementsmaybeinconsistent,andhowtomeasureinconsistencyandimprovethejudgements,whenpossibletoobtainbetterconsistencyisaconcernoftheAHP.Thederivedpriorityscalesaresynthesisedbymultiplyingthembythepriorityoftheirparentnodesandaddingforallsuchnodes.Anillustrationisincluded.Keywords:decisionmaking;intangibles;judgements;prioritiesAnalyticHierarchyProcess;AHP;comparisons;ratings;synthesis.Referencetothispapershouldbemadeasfollows:Saaty,T.L.(2008)‘Decisionmakingwiththeanalytichierarchyprocess’,Int.J.ServicesSciences,Vol.1,No.1,pp.83–98.Biographicalnotes:ThomasL.SaatyholdstheChairofUniversityProfessorattheUniversityofPittsburghandisaMemberoftheNationalAcademyofEngineering,USA.Heisinternationallyrecognisedforhisdecision-makingprocess,theAnalyticHierarchyProcess(AHP)anditsgeneralisationtonetworkdecisions,theAnalyticNetworkProcess(ANP).HewontheGoldMedalfromtheInternationalSocietyforMulticriteriaDecisionMakingforhiscontributionstothisfield.Hisworkisindecisionmaking,planning,conflictresolutionandinneuralsynthesis.1IntroductionWeareallfundamentallydecisionmakers.Everythingwedoconsciouslyorunconsciouslyistheresultofsomedecision.Theinformationwegatheristohelpusunderstandoccurrences,inordertodevelopgoodjudgementstomakedecisionsabouttheseoccurrences.Notallinformationisusefulforimprovingourunderstandingandjudgements.Ifweonlymakedecisionsintuitively,weareinclinedtobelievethatallkindsofinformationareusefulandthelargerthequantity,thebetter.Butthatisnottrue.Therearenumerousexamples,whichshowthattoomuchinformationisasbadaslittleinformation.Knowingmoredoesnotguaranteethatweunderstandbetterasillustratedbysomeauthor’swriting“Expertafterexpertmissedtherevolutionarysignificanceof84T.L.SaatywhatDarwinhadcollected.Darwin,whoknewless,somehowunderstoodmore”.Tomakeadecisionweneedtoknowtheproblem,theneedandpurposeofthedecision,thecriteriaofthedecision,theirsubcriteria,stakeholdersandgroupsaffectedandthealternativeactionstotake.Wethentrytodeterminethebestalternative,orinthecaseofresourceallocation,weneedprioritiesforthealternativestoallocatetheirappropriateshareoftheresources.Decisionmaking,forwhichwegathermostofourinformation,hasbecomeamathematicalsciencetoday(Figueraetal.,2005).Itformalisesthethinkingweusesothat,whatwehavetodotomakebetterdecisionsistransparentinallitsaspects.Weneedtohavesomefundamentalunderstandingofthismostvaluableprocessthatnatureendoweduswith,tomakeitpossibleforustomakechoicesthathelpussurvive.Decisionmakinginvolvesmanycriteriaandsubcriteriausedtorankthealternativesofadecision.Notonlydoesoneneedtocreateprioritiesforthealternativeswithrespecttothecriteriaorsubcriteriaintermsofwhichtheyneedtobeevaluated,butalsoforthecriteriaintermsofahighergoal,oriftheydependonthealternatives,thenintermsofthealternativesthemselves.Thecriteriamaybeintangible,andhavenomeasurementstoserveasaguidetorankthealternatives,andcreatingprioritiesforthecriteriathemselvesinordertoweightheprioritiesofthealternativesandaddoverallthecriteriatoobtainthedesiredoverallranksofthealternativesisachallengingtask.How?Inthelimitedspacewehave,wecanonlycoversomeoftheessentialsofmulticriteriadecisionmaking,leavingittothereadertolearnmoreaboutitfromtheliteraturecitedattheendofthispaper.Themeasurementofintangiblefactorsindecisionshasforalongtime,defiedhumanunderstanding.Numberandmeasurementarethecoreofmathematicsandmathematicsisessentialtoscience.Sofar,mathematicshasassumedthatallthingscanbeassignednumbersfromminusinfinitytoplusinfinityinsomeway,andallmathematicalmodellingofrealityhasbeendescribedinthiswaybyusingaxesandgeometry.Naturally,allthisispredicatedontheassumptionthatonehastheessentialfactorsandallthesefactorsaremeasurable.Buttherearemanymoreimportantfactorsthatwedonotknowhowtomeasurethanthereareonesthatwehavemeasurementsfor.Knowinghowtomeasuresuchfactorscouldconceivablyleadtonewandimportanttheoriesthatrelyonmanymorefactorsfortheirexplanations.Afterall,inaninterdependentuniverseeverythingdependsoneverythingelse.Isthisjustaplatitudeoristheresometruthbehindit?Ifweknewhowtomeasureintangibles,muchwiderroomwouldbeopentointerpreteverythingintermsofmanymorefactorsthanwehavebeenabletodosofarscientifically.Onethingisclear,numericalmeasurementmustbeinterpretedformeaningandusefulnessaccordingtoitsprioritytoserveourvalues