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MarcinAnholcer
ALGORITHMFORDERIVINGPRIORITIES
FROMINCONSISTENT
PAIRWISECOMPARISONMATRICES
Abstract
InseveralmultiobjectivedecisionproblemsPairwiseComparisonMatrices
(PCM)areappliedtoevaluatethedecisionvariants.Theproblemthatarisesveryoften
isinconsistenceofgivenPCM.Insuchasituationitisimportanttoapproximate
thePCMwithaconsistentone.ThemostcommonwayistominimizetheEuclidean
distancebetweenthematrices.Inthepaperweconsiderminimizationofthemaximum
distance.
Keywords
Heuristics,nonlinearprogramming,decisionmaking,pairwisecomparison.
Introduction
Oneofthepopulartoolsofmultiobjectivedecisionmakingisthe
AnalyticHierarchyProcess,introducedbySaaty[seee.g.Saaty1980;Erkut
andTarimcilar1991]andstudiedbynumerousauthors.Duringtheprocess,
theDecisionMakercomparespairwisengivendecisionvariants.Usually
thecomparisonsarerepresentedbythepairwisecomparisonmatrixA=[aij],
wherethenumberaijsayshowmanytimesthevariantiispreferred
tothevariantj.
Thevaluesofaij,i=1,2,…,n,j=1,2,…,nshouldfulfillthefollowing
conditions:
.
a.j
1
aj.
for.
.1,2,…,n,j.1,2,…,n,
a.jajk.a.kfor.
.1,2,…,n,j.1,2,…,n,k.1,2,…,n.
(1)
(2)
