Multicriteria Methodology for Decision Aiding

303 Pages·1996·7.17 MB·English

by  Bernard Roy (auth.)

Multicriteria Methodology for Decision Aiding
Nonconvex Optimization and Its Applications
Volume 12
Managing Editors:
Panos Pardalos
University ofFlorida, U.S.A.
Reiner Horst
University ofTrier, Gerrnany
Advisory Board:
Ding-ZhuDu
University ofM innesota, U.S.A.
C.A. Floudas
Princeton University, U.S.A.
G.Infanger
Stanford University, U.S.A.
J.Mockus
Lithuanian Acaderny of Sciences, Lithuania
P.D. Panagiotopoulos
Aristotle University, Greece
H.D. Sherali
Virginia Polytechnic Institute and State University, U.S.A.
The titZes published in this series are listed at the end ofthis volurne.
Multicriteria
Methodology for
Decision Aiding
by
BemardRoy
LAMSADE, Universite Paris-Dauphine
Translator
Mark R. McCord
The Ohio State University, U.SA
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4419-4761-1 ISBN 978-1-4757-2500-1 (eBook)
DOI 10.1007/978-1-4757-2500-1
Printed on acid-free paper
All Rights Reserved
© 1996 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1996
Softcover reprint ofthe hardcover 1st edition 1996
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
inc1uding photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
Table of Contents
Reader's Guide ............................................. xiii
Foreword for the English-language edition ......................... xv
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
INTRODUCTORY CHAPTERS: HOW TO AID WHOM WITH
WHAT TYPES OF DECISIONS
Chapter 1: Decision Problems and Processes ......................... 3
Summary ..................... " ............................ 3
Chapter 2: Decision Aiding: Major Actors and the Role of Models ........ 7
Summary ................................................... 7
2.1 Models and Realities ........................................ 7
2.1.1 Definition ............................................ 7
2.1.2 Limiting the scope of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 8
2.1.3 The family of questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9
2.1.4 The model as representation ............................... 9
2.2 Decision Aiding ......................................... " 10
2.2.1 Definition ........................................... 10
2.2.2 Aiding for whom? ..................................... 11
2.2.3 Aiding by whom? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12
2.2.4 Presence of a dient .................................... 13
2.2.5 Aid and neutrality ..................................... 14
2.2.6 Aid and objectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15
Chapter 3: Reference Examples ................................. 19
Summary .................... '" ......................... " 19
3.1 Infrastructure Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19
3.2 National or Regional Development Problems. . . . . . . . . . . . . . . . . . . . . .. 21
3.3 Advertising Problems ....................................... 23
3.4 Research and Development Problems ............................ 24
3.5 Operations Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 25
3.6 Selection Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28
3.7 Manufacturing Problems ..................................... 29
vi Table 0/ Contents
Chapter 4: Phases and Options of an Approach to Decision Aiding
(General Ideas of the Methodology) . . . . . . . . . . . . . . . . . . . . .. 31
Summary .................................................. 31
4.1 Notions of Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 31
4.1.1 Preliminaries ......................................... 31
4.1.2 Study phase and decision process development state . . . . . . . . . . . . .. 33
4.2 The Proposed Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34
4.2.1 Level I: Object of the decision and spirit of recommendation
or participation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34
4.2.2 Level 11: Analyzing consequences and developing criteria . . . . . . . . .. 35
4.2.3 Level III: Modeling comprehensive preferences and operationally
aggregating performances ................................ 36
4.2.4 Level IV: Investigating and developing the recommendation ........ 36
4.2.5 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 37
LEVEL I: HOW TO DETERMINE WHAT IS POSSIBLE AND IN WHAT
TERMS TO FORMULATE A PROBLEM . . . . . . . . . . . . . . . .. 39
Chapter 5: Actions and Decision Aiding ........................... 41
Summary .................................................. 41
5.1 The Concept of an Action. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 41
5.1.1 Definition and examples ................................. 41
5.1.2 Comprehensive and fragmented conceptions: identification problems .. 44
5.2 The Set of Potential Actions .................................. 47
5.2.1 Delimiting the set of possible actions ........................ 47
5.2.2 Examples ........................................... 49
Chapter 6: Problematics as Guides in Decision Aiding . . . . . . . . . . . . . . . .. 57
Summary .................................................. 57
6.1 The Four Reference Problematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 57
6.1.1 Choice problematic P .u: Help choose a "best" action or develop a
selection procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 58
6.1.2 Sorting problematic P.ß: Help sort actions according to norms or build
an assignment procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 62
6.1.3 Ranking problematic P.y Help rank actions in order of decreasing
preference or build an ordering procedure ........... . . . . . . . . .. 64
6.1.4 Description problematic P.b: Help describe actions and their
consequences in a formalized and systematic manner or develop a
cognitive procedure .................................... 68
6.2 Remarks on Choosing the Problematic ........................... 69
6.2.1 Factors influencing the choice of problematic ................. \ 69
6.2.2 Examples ........................................... 70
6.2.3 Multiple cases ........................................ 73
Table of Contents vii
LEVEL 11: HOW TO DETERMINE PREFERENCES AND ON WHAT
BASES ........................................... 75
Chapter 7: Preference, Indifference, Incomparability: Binary Relations
and Basic Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 79
Summary .................................................. 79
7.1 General Comments on Preference Modeling: Basic Concepts . . . . . . . . . . .. 81
7.1.1 Basic preference situations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 81
7.1.1.1 Introductory examples ............................. 81
7.1.1.2 Basic situations and the axiom of limited comparability ...... 84
7.1.2 Modeling with binary relations: System of preference relations ...... 86
7.1.2.1 Notation and terminology ........................... 86
7.1.2.2 Systems of preference relations and the axiom of limited
comparability ................................... 88
7.1.2.3 Comments on incomparability and weak preference . . . . . . . .. 91
7.1.2.4 Comments on the transitivity of the basic binary relations .... 91
7.1.3 Consolidated situations and associated binary relations ............ 92
7.1.3.1 General comments ................................ 92
7.1.3.2 Preference and nonpreference: Perfect system of preference
relations ....................................... 93
7.1.3.3 J-preference, K-preference, basic system of outranking
relations ....................................... 95
7.1.3.4 Links among these and other relations .................. 97
7.2 Principal Structures and Functional Relations. . . . . . . . . . . . . . . . . . . . . .. 98
7.2.1 Graphical representations and an example system of preference
relations ............................................ 99
7.2.1.1 Graph theory: Notation. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 99
a) General notation ............................... 99
b) Notation for systems of preference relations ............ 100
7.2.1.2 A new example: The mayor's preferences ................ 101
7.2.2 Basic structures of SPR's that exclude or obscure incomparability .... 105
7.2.2.1 SPR's with only one relation ......................... 105
a) Equivalence classes ............................. 105
b) Complete orders and intransitive tournaments . . . . . . . . . . . 106
bl) Definitions . ................................ 106
b2) Functional representation of a complete order . ....... 107
c) Two-relation structures: a first look at complete basic
systems of outranking relations (BSOR) ............... 108
7.2.2.2 SPR's with two relations ........................... 108
a) Complete preorders ............................. 108
al) Nonfunctional representation .................... 108
a2) Functional representation ...................... 109
b) Structure of a semi-order ......................... 111
bl) Example .................................. 111
b2) Semi-order properties ......................... 112
viii Table of Contents
b3) Definition and functional representation . . . . . . . . . . . . 114
c) Other structures with one symmetrie and one asymmetrie
relation . ..................................... 114
cl) Comparison of interval-actions .................. 115
c2) Definitions and special cases . . . . . . . . . . . . . . . . . . . . 116
7.2.2.3 SPR's with three or more relations ..................... 116
a) System (I, P, Q) on interval actions .................. 116
b) Pseudo-order structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
b l) Example .................................. 117
b2) Definition and nonfunctional representations ......... 118
b3) Functional representation ...................... 119
c) Directed semi-order structure ...................... 120
cl) Definition ................................. 120
c2) Similarities with semi-orders and functional
representation .............................. 121
7.2.3 Basic structures of SPR's with incomparability ................. 122
7.2.3.1 General comments ................................ 122
7.2.3.2 Partial preorders ................................. 122
7.2.3.3 Other (R, T, V) structures ........................... 123
7.2.4 Comparing preference differences or exchanges . . . . . . . . . . . . . . . . . 124
a) Examples and discussion ......................... 124
b) Preference relations on A x A ...................... 126
Chapter 8: Comparing Actions and Modeling Consequences ............ 127
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
8.1 Consequences of an Action, Dimensions, and Associated State Indicators ... 128
8.1.1 The consequence cloud .................................. 128
8.1.2 Elementary consequences ................................ 130
8.1.2.1 General remarks on modeling the consequence cloud ........ 130
8.1.2.2 lllustrations and practical considerations . . . . . . . . . . . . . . . . . 132
8.1.3 Scales and dimensions .................................. 132
8.1.3.1 Methodological perspective: Definitions and illustrations ..... 132
8.1.3.2 Types of scales and practical considerations .............. 134
8.1.4 State indicators and consequence spectrum .................... 135
8.1.5 Examples ........................................... 137
8.2 Evaluating an Action: Dispersion Indicators to Model Imprecision,
Uncertainty, and Inaccurate Determination ......................... 144
8.2.1 Lack of knowledge and state indicator deficiencies ............... 145
8.2.2 Dispersion thresholds ................................... 148
8.2.2.1 Intrinsic and nonintrinsic dispersion thresholds ............ 148
8.2.2.2 Dispersion thresholds and indicators .................... 150
8.2.2.3 Properties of intrinsic dispersion thresholds ............... 151
8.2.3 Modulated dispersion indicators (or modulation indicators) ......... 152
8.2.3.1 Dispersion factors determined from subjective opinions allowing
distinctions in state importance or likelihood .............. 153
Table 0/ Contents ix
8.2.3.2 Dispersion factors determined from objective observations
allowing qualitative modulation of state importance or
likelihood ...................................... 155
8.2.3.3 Dispersion factors represented by distributions of
nonrandom magnitudes allowing quantitative modulation of
state importance or likelihood ........................ 157
8.2.3.4 Dispersion factors represented by probability distributions
allowing quantitative modulation of state importance or
likelihood ...................................... 157
8.2.3.5 General form of modulation indicators: ordinal modulation and
additive modulation ............................... 157
8.2.4 Referenced dispersion indicator ............................ 158
8.2.5 Evaluating an action: Principles of c1arity, universality, and reliability . 160
Chapter 9: Comparing Actions and Developing Criteria ............... 163
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
9.1 The Concept of Criterion ..................................... 164
9.1.1 Criteria and functions: General remarks ...................... 164
9.1.2 Definition and comments ................................. 167
9.2 Constructing Criteria from Consequences ......................... 170
9.2.1 Criterion function with one dimension and a point state indicator . . . . . 170
9.2.2 Criteria with one dimension and a nonpoint state indicator ......... 172
9.2.2.1 Point reduction on the dimension . . . . . . . . . . . . . . . . . . . . . . 173
a) Point reduction based on an average or aglobai mass .... 173
al) Examples and basic formulas . . . . . . . . . . . . . . . . . . . . 173
a2) Basic remarks and a first look at utility theory ....... 174
b) Point reduction based on percentiles or on other dispersion
characteristics ................................. 176
c) Point equivalent: another look at utility theory .......... 177
9.2.2.2 Splitting dimension i .............................. 178
9.2.3 Criterion function based on a subset of dimensions ............... 180
a) One dimension is dominant among the I dimensions ...... 181
b) I consists of two or three dimensions whose scales can be
reduced to a few degrees ......................... 182
c) The elementary consequences associated with I are evaluated
on the same scale Ei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
d) The elementary consequences associated with I lead to a
natural synthesis for reasons other than those given in
a), b), c) ..................................... 182
9.3 True Criteria, Semi-Criteria, Pre-Criteria, Pseudo-Criteria .............. 184
9.3.1 True criterion and discriminating power of a criterion ............. 184
9.3.2 Indifference and preference thresholds ....................... 188
9.3.3 Pseudo-criteria, semi-criteria, pre-criteria ...................... 191
9.3.4 Determining indifference and preference thresholds .............. 193
a) General remarks ............................... 193