Theanalytichierarchyprocess(AHP)isusedwidelyforanalyzingdecisionsmadeinvariousreal-worldapplications.Itsbasicideaistoconstructahierarchyofconceptsencounteredinagivendecisionproblemandtochoosethebestalternativeaccordingtopairwisecomparisonmatricesgivenbythedecisionmaker.Undertheassumptionoffullyrationaleconomics,areasonabledecisionshouldbeconsistent.Itbecomesanimportantissueonhowtoanalyzeandensuretheconsistencyofcomparisonmatricestogetherwiththejudgmentsofthedecisionmaker.Themainobjectivesofthepresentpaperarethreefold.First,wereviewthebasicideaandmethodsusedtodefinetheconsistencyandthetransitivityofmultiplicativereciprocalmatrices,additivereciprocalmatricesandcomparisonmatriceswithfuzzyintervalandtriangularfuzzynumbers.TheexistingcontroversybehindtheapplicationsoffuzzysettheorytotheAHPintheliteratureispresented.Second,theconsistencyofthecollectivecomparisonmatricesingroupdecisionmakingbasedonAHPandfuzzyAHPisfurtheranalyzed.WepointoutthattheweakconsistencyofpreferencerelationswithfuzzynumbersinfuzzyAHPandgroupdecisionmakingshouldbeinvestigatedcomprehensively.Third,undertheconsiderationofthevaguenessintheprocessofevaluatingthejudgements,anewconceptoffuzzyconsistencyofcomparisonmatricesintheAHPisgiven.
