Data Processing for the AHP/ANP

141 Pages·2013·1.46 MB·English

by  Gang Kou

Quantitative Management
Forfurthervolumes:
http://www.springer.com/series/10621

Gang Kou • Daji Ergu (cid:129) Yi Peng (cid:129) Yong Shi
Data Processing for the
AHP/ANP
123
GangKou DajiErgu
SchoolofManagementandEconomics CollegeofElectricalandInformation
UniversityofElectronicScience Engineering
andTechnologyofChina SouthwestUniversityforNationalities
NorthJiansheRoad YihuanRoad
Chengdu Chengdu
China,People’sRepublic China,People’sRepublic
YiPeng YongShi
SchoolofManagmentandEconomics UniversityofNebraskaatOmahaIS&T
UniversityofElectronicScience DodgeStreet
andTechnologyofChina OmahaNebraska
NorthJiansheRoad USA
Chengdu
China,People’sRepublic
ISSN2194-086X ISSN2194-0878 (electronic)
ISBN978-3-642-29212-5 ISBN978-3-642-29213-2(eBook)
DOI10.1007/978-3-642-29213-2
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2012944253
©Springer-VerlagBerlinHeidelberg2013
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Abstract
The positive reciprocal pairwise comparison matrix (PCM) is a well established
techniqueandwidelyusedinmultiplecriteriadecisionmaking(MCDM)methods
toperformpairwisecomparisonsandderivetheweightvectorsofbeingcompared
items, especially in the analytical hierarchy (network) process (AHP/ANP). The
PCM is also used to quantifythe qualitativeand/orintangibleattributes into mea-
surablequantities.Consistencytest,inconsistentdataidentificationandadjustment,
missing or uncertain data estimation, and sensitivity analysis of rank reversal are
importantresearchissuesinthisfield.Althoughtheseissueshavebeenextensively
studied, there is no universally accepted, simple and generalized data processing
model to handle the above mentioned issues simultaneously. In this book, the
maximum eigenvalue threshold method is proposed as the new consistency index
forthe AHP/ANP. An inducedbias matrixmodel(IBMM) is proposedto identify
andadjusttheinconsistentdata,andestimatethemissingoruncertaindata.Based
on the IBMM, several questionnaire design improvement formats are proposed
to quickly collect the data to make rapid and efficient decision making. Besides,
the IBMM is further used to analyze the sensitivity of rank reversal issue when
addingnewcriteriaoralternativesordeletingoldcriteriaoralternatives.Finally,two
applicationsofIBMM,taskschedulingandresourceallocationincloudcomputing
environment, and risk assessment and decision analysis, are used to illustrate the
proposedIBMM. As anextendedmodelofIBMM, aninducedarithmeticaverage
biasmatrix(IAABM)isdescribedindetailinfinalChapter.
v

Keywords
The analytical hierarchy (network) process (AHP/ANP), Induced bias matrix
model(IBMM),Dataprocessing,Consistencytest,Maximumeigenvaluethreshold,
Inconsistencyidentificationandadjustment,Uncertainormissingvaluesestimation,
Rankreversal,Inducedarithmeticaveragebiasmatrix(IAABM).
vii

Contents
1 Introduction .................................................................. 1
References..................................................................... 5
2 ANewConsistencyTestIndexfortheDataintheAHP/ANP .......... 11
2.1 BasicsoftheAHP/ANP ................................................ 11
2.1.1 ThePositiveReciprocalPairwiseComparisonMatrix........ 11
2.1.2 BasicsoftheAHP .............................................. 13
2.1.3 BasicsoftheANP .............................................. 14
2.2 ConsistencyTestIssueintheAHP/ANP............................... 16
2.2.1 AnalysisoftheConsistencyRatio(CR)Method.............. 16
2.2.2 TheIssuesofConsistencyTestintheAHP/ANP............. 17
2.3 TheNew ConsistencyIndex:MaximumEigenvalue
ThresholdfortheAHP/ANP ........................................... 18
2.3.1 The Advantagesof Maximum Eigenvalue
ThresholdforAHP/ANP....................................... 20
2.4 TheProcessesofDataConsistencyTestinAHP/ANP................ 21
2.5 IllustrativeExample..................................................... 25
References..................................................................... 27
3 IBMMforInconsistentDataIdentificationandAdjustment
intheAHP/ANP.............................................................. 29
3.1 TheTheoremsofInducedBiasMatrixModel(IBMM) .............. 29
3.1.1 TheTheoreticalProofsofIBMM.............................. 31
3.2 IBMMforInconsistentDataIdentificationandAdjustment.......... 40
3.2.1 TheBasicsoftheInconsistencyIdentification
andAdjustmentMethod........................................ 40
3.2.2 TheProcessesofInconsistencyIdentification
andAdjustmentMethod........................................ 41
3.2.3 FastInconsistencyIdentificationandAdjustmentMethod ... 44
3.3 IllustrativeExamples.................................................... 50
3.3.1 IllustrativeExamplesforGeneralInconsistency
IdentificationandAdjustmentMethod ........................ 50
ix
x Contents
3.3.2 IllustrativeExamplesfor FastInconsistency
IdentificationandAdjustmentMethod ........................ 62
References..................................................................... 64
4 IBMMforMissingDataEstimation....................................... 65
4.1 BasicsoftheIBMMforMissingDataEstimation .................... 65
4.2 TheProcessesofEstimatingMissingDatabytheIBMM ............ 66
4.3 ProofsoftheIBMMforIPCMinOrderThree........................ 68
4.4 IllustrativeExamples.................................................... 71
4.4.1 IllustrativeExamplesinOrderThree.......................... 71
4.4.2 IllustrativeExamplesinOrderFour ........................... 73
References..................................................................... 75
5 IBMMforQuestionnaireDesignImprovement .......................... 77
5.1 MotivationoftheResearch............................................. 77
5.2 ThePrinciplesofImprovingtheQuestionnaireDesign............... 79
5.3 IllustrativeExample..................................................... 83
References..................................................................... 91
6 IBMMforRankReversal................................................... 93
6.1 RankReversalIssueintheAHP/ANP................................. 93
6.2 SensitivityAnalysisofRankReversalbytheIBMM ................. 94
6.3 IllustrativeExamples.................................................... 94
References..................................................................... 105
7 ApplicationsofIBMM....................................................... 107
7.1 Task SchedulingandResourceAllocationin Cloud
ComputingEnvironmentbytheIBMM................................ 107
7.1.1 ResourceAllocationinCloudComputing..................... 108
7.1.2 Task-OrientedResourceAllocationinCloudComputing.... 109
7.1.3 IllustrativeExamples ........................................... 110
7.2 RiskAssessmentandDecisionAnalysisbytheIBMM............... 116
7.2.1 BackgroundofRiskAssessmentandDecisionAnalysis..... 116
7.2.2 IllustrativeExamples ........................................... 116
References..................................................................... 126
8 InducedArithmeticAverageBiasMatrixModel(IAABMM).......... 129
8.1 TheTheoremofIAABMM............................................. 129
8.2 TheInconsistencyIdentificationProcessesofIAABMM............. 130
8.3 TheEstimatingFormulaofInconsistencyAdjustment................ 132
8.4 IllustrativeExamples.................................................... 133
References..................................................................... 135
Index............................................................................... 137