A
absolute-any (AA) critical criterion 134, 141, 152
absolute terms 133
absolute-top (AT) critical criterion 134, 141, 151
actual relative weights 98
additive function 228
additive utility assumption 6-7
AHP axioms 215
AHP variant by Dyer 222-223
all possible comparisons 105-112
alternatives 1
analytic hierarchy process (AHP) 9-11, 116, 137-141, 157-160,
165-166, 179-182, 186-188, 197-199,
201-212, 215-217, 225-227, 241
attributes 2
available comparisons 105-112
average consistency index of CDP matrices 41-42
average squared residual 65
B
best scales 51, 53
best MCDM method 199
best fuzzy MCDM method 261-262
bound of maximum consistency 40
"Bridge Evaluation" problem 230-231
C
case studies 230-232
common characteristic 74
common comparisons 105-112
complete pairwise comparisons 88
conflict among criteria 1
concordance index 14, see also TOPSIS (fuzzy and crisp)
concordance matrix 16, see also TOPSIS (fuzzy and crisp)
concordance set 16, see also under TOPSIS (fuzzy and crisp)
consistency see perfect consistency
consistency index (CI) 59, 67-71
consistency of CDP matrices 35-42
consistency ratio (CR) 59
consistent data 91
"city-block-metric" 74
class 1 scales 45-47
class 2 scales 45, 48-49
Closest Discrete Pairwise (CDP) matrix 32-43, 80, 98, 145, 202, 251
closest value 34
critical alternatives (most) 156-175
criticality degree (of a decision criterion) 136
criticality degree (of an alternative) 156
criticality degree (of measures of performance) 160, 164
critical measure of performance (most) 155-175
Criterium Decision Plus (computer software) 201, 212
D
decision criteria 1
decision making paradox see paradox
decision matrix 2-3
decision space 1
decision support tool 207
decision weights 2
decomposition of judgment matrices 88-113
definiteness property 74
descriptive theories 265
deterministic MCDM 2
difference comparisons 74-86
difference judgments 76-86
dimensionless analysis 8
discordance index 14, see also TOPSIS (fuzzy and crisp)
discordance matrix 16-17, see also TOPSIS (fuzzy and crisp)
discordance set 16, see also TOPSIS (fuzzy and crisp)
discrete decision spaces 1
dissimilarity relation 74
distance (of similarity) 74
dominance matrices 17-18, see also TOPSIS (fuzzy and crisp)
duality approach 115-129
dual problem see duality approach
E
eigenvalue approach 44, 58-59, 217
eigenvector see eigenvalue approach
eigenvector approximation 58-59
see eigenvalue approach
eigenvector method see eigenvalue approach
ELECTRE method 13-18, 241
error terms 93
evaluative criteria (crisp) 43, 177-199
evaluative criteria (fuzzy) 250-262
Euclidean distance 19-20
examples of exponential scales 29-32
Expert Choice 132, 201, 212
exponential scales 24, 28-32
H
hierarchic composition 214
hierarchies (multiple) 131
hierarchical structure 1
human rationality assumption 61-71
F
feasible solution 85
feasible value 137, 163
"flat maxima principle" 131
fuzzy AHP 245-247, 262
fuzzy alternatives 236, 239, 242-262
fuzzy decision criteria 236, 242-262
fuzzy CDP matrix 251-257
fuzzy data 235
fuzzy databases 87
fuzzy decision matrix 243, 254-256
fuzzy evaluative criteria see evaluative criteria
fuzzy operations 236-329
fuzzy MCDM 2, 241-262
fuzzy numbers 166, 236-237, 239, 241
fuzzy RCP matrix 251-257
fuzzy reciprocal (judgment) matrix 253-260
fuzzy revised AHP 247-248, 258, 262
fuzzy sets 57, 87
fuzzy TOPSIS 248-250, 262
fuzzy trapezoid numbers 237
fuzzy triangular numbers see fuzzy numbers
fuzzy WSM 242-244, 262
fuzzy WPM 244-245, 262
G
goals 1-2
group decision making 2
guided (pairwise comparisons) 88
Q
quadratic problem see quadratic programming
quadratic programming 75, 79-85
I
ideal mode AHP see, revised AHP
ideal solution 20
identical alternatives 214
incommensurable units 2
inconsistent CDP matrix 37
InfoHarvest, Inc. 201
L
Langrangian multipliers 81
Langrangian (the) 81
large size decision problems 128
law of stimulus of measurable magnitude 26
law of stimulus perception 28
least squares 63-67
linguistic choices 24, 28
linear equation, system of 79, 82
linear programming 92-97, 112
linear scale 24, see also Saaty scale
Lootsma scales see exponential scales
logical contradiction 222
M
matrix partitioning see decomposition
matrix transpose 82
maximum eigenvalue see eigenvalue approach
maximum similarity 73-74
maximum dissimilarity 73-74
maximum consistency of CDM matrices 38-42
maximum consistency index 40-42
membership value 57, also see fuzzy numbers
modal value 237
most critical criterion 133-135, 138-139, 141
most important criterion 144
most sensitive alternative 155-156
missing pairwise comparisons 86, 91
Multi-Attribute Decision Making (MADM) 1
multi-attribute utility theory (MAUT) 214
Multi-Criteria Decision Making (MCDM) (definitions) 1-22
multi-dimensional MCDM 8
Multi-Objective Decision Making (MODM) 1
multiple attributes 1
multiple hierarchies 131-132
multiple objective functions 1
multiplicative AHP 228-233, see also WPM
N
negative-ideal solution 20
normalized decision matrix 14-16, 19
normalized columns 117-118
normalized rows 117-118
normative theories 265
number of alternatives (role of) 207
O
optimization approaches 60-67
optimal solution 83-85
outranking relations 13-14
P
pairwise comparisons 23, 25-32
paradox 2, 42, 145, 197-199, 265
partial ranking 221
partitioning of pairwise comparisons 90,
see also decomposition of judgment matrices
percent-any (PA) critical criterion 134-135, 140-141, 145, 150
percent-top (PT) critical criterion 134-135, 140-141, 145, 149
perfect consistency 95, 215, 218
performance values see decision matrix
power law 32
power method 67
prescriptive theories 265
prime approach see duality approach
prime problem see duality approach
primal approach see duality approach
R
random consistency index (RCI) 59, see also consistency index
ranking abnormalities 213-233
ranking of fuzzy numbers 238-239
ranking reversal 43
ranking indiscrimination 43
ratio comparisons 57-72
Real Continuous Pairwise (RCP) matrix 32-34, 80, 97, 146,
202-205, 251
real life case studies 230-232
reciprocal comparisons see pairwise comparisons
reciprocal matrices 88-89, see also pairwise comparisons
redundant constraints 96
relative closeness 20
relative importance 75, 85
relative priorities 89, see also relative importance
relative magnitudes 25
relative ranking 80
relative similarity 75-85, also, see similarity
relative terms 132
relative weights 57-72, 73-86, 87-113
revised AHP 11-13, 116, 189, 191-193, 197-199,
201-212, 214, 218-222, 225-227
robust criterion 138
robust decision problem 164
S
Saaty scale 26-27
scale 24-55, 75
scale generation 27
scale evaluation 32-55
separation measure 20
SENSATTO library 131
sensitivity analysis 131-175
sensitivity coefficient (of a criterion) 136
sensitivity coefficient (of an alternative) 156
sensitivity coefficient (of measures of performance) 160, 164
similarity function 73
similarity scale 77
similarity measure 74
single-dimensional MCDM 8
"Site Selection" problem 232
stepwise approach 166
stochastic MCDM 2
stimulus of measurable magnitude 26
stimulus perception 28
symmetric comparisons see difference judgments
symmetric comparisons 76
system of linear equations see quadratic programming
T
taxonomy of MCDM methods 4
threshold value(s) 155, 158-159, 161, 163, 175
TOPSIS method 18-21, 194-196, 241
triangular property 74, 85
V
"vector-maximum" problem 1
U
union operation 87
units of measure 8
upper bound of reduction rate 120
unrestricted variables 93
utility theory 214
W
weighted product model (WPM) 8-9, 142-145, 154, 161-164, 165,
169-170, 174-175, 180, 183, 185,
192, 197-199, 228-233, 241
weighted sum model (WSM) 6-7, 137-141, 157-160, 165, 167-168,
170-171, 179-185, 241, 197-199
worst scales 52-54