Multi-Criteria Decision Making Methods: A Comparative Study

by Evangelos Triantaphyllou, Ph.D.

SUBJECT INDEX



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



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