Data Processing for the AHP/ANP
The positive reciprocal pairwise comparison matrix (PCM) is one of the key components which is used to quantify the qualitative and/or intangible attributes into measurable quantities. This book examines six understudied issues of PCM, i.e. consiste
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A Analytical hierarchy process (AHP), 1–5, 7–57, 61, 62, 72, 78, 87, 90, 102, 103, 110, 115 Analytical network process (ANP), 3–5, 7–57, 61, 62, 72, 87, 90, 110, 111, 115
B Bias distribution, 123, 127 Bias identifying vector, 35, 36, 45, 47, 48, 50, 52, 53 Block diagonal matrix, 17–22, 110, 111, 114–116
C Cardinal consistency, 2 Cloud computing, 101–109 Consistency ratio (CR), 8, 10, 12–16, 19, 22 Consistency test index, 5 Constraint system of equations, 89
D Data consistency test, 17–21 Decision analysis, 110–119 Differentiated services, 73, 75
E Estimating formula, 124–127 Estimating the missing values, 72, 73, 75, 84
F Fast inconsistency identification, 38–44, 56
I Importance of score items, 75 Improvement of questionnaire design, 71–85 Incomplete pairwise comparison matrix (IPCM), 60–64 Incomplete pairwise comparison matrix (PCM), 3 Inconsistency adjustment, 124–127 Inconsistency identification, 5, 106, 108, 111, 115, 122–127 Inconsistent data adjustment, 23–57 Inconsistent data identification, 23–57 Induced arithmetic average bias matrix model (IAABMM), 121–127 Induced bias matrix (IBM), 88, 98, 121, 124–126 Induced bias matrix model (IBMM), 23–57, 59–69, 71–85, 87–99, 101–119 Inner-cluster, 13, 14
L Level-by-level test, 19, 21 Linear or nonlinear equations, 61 Lower triangular matrix, 61, 63, 68, 69
M Matrix order reduction, 35–38, 45, 51 Maximal eigenvalue, 122 Maximum eigenvalue threshold, 14–17, 19, 22 Method of maximum, 36 Method of minimum, 36, 48 Minimize all bias entries, 61–63, 65, 66, 68 Missing data estimation, 59–69 Missing values estimation, 4, 5, 59–62, 64, 66–68
G. Kou et al., Data Processing for the AHP/ANP, Quantitative Management 1, DOI 10.1007/978-3-642-29213-2, © Springer-Verlag Berlin Heidelberg 2013
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138 Multiple criteria decision making (MCDM), 1, 110
N Negative largest value, 123 Non-zero rows (columns) and sign identification, 43–44, 57
O Outer-cluster, 13, 14
P Pairwise comparison matrix (PCM), 1–5, 72–75, 77–79, 81, 83–85, 121 Positive reciprocal matrix, 1 Preference conflict, 77 Priority vectors, 88
Q Questionnaire design, 5 Questionnaire survey, 73, 75, 76, 81, 83, 84
Index R Rank reversal, 5, 87–99 Resource allocation, 101–109 Reversal points, 88, 98 Risk assessment, 110–119
S Scalar product of vectors, 34 Sensitivity analysis, 87, 88, 90–97, 99 Supermatrix of a network, 12, 13
T Task scheduling, 101–109 Typical hierarchy structure, 9, 17, 18, 21
U Uncertain score factor, 77 Unknown variables, 88 Upper triangular matrix, 61, 62
W Whole-level test, 20, 21
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