Evaluation And Decision Models With Multiple Criteria

by Bouyssou, Denis; Marchant, Thierry; Pirlot, Marc; Tsoukias, Alexis; Vincke, Philippe

• ISBN13: 9780387310985
• ISBN10: 0387310983
• Format: Hardcover
• Copyright: 2006-02-06
• Publisher: Springer Verlag

Summary

Formal decision and evaluation models are sets of explicit and well-defined rules to collect, assess, and process information in order to be able to make recommendations in decision and/or evaluation processes. They are so widespread that almost no one can pretend not to have used or suffered the consequences of one of them.In our earlier companion volume, Evaluation and Decision Models, we heavily criticised formal models but we also argued that they could be useful. On the other hand, Evaluation and Decision Models with Multiple Criteria is a guide, a way of reasoning aimed at helping the analyst to choose a model and use it consistently. We propose, often using an axiomatic point of view, a sound analysis of techniques aimed at supporting the decision aiding process. Our presentation is carried out within a unique framework that can be extended to most decision and evaluation models, as a "decision aiding methodology".Evaluation and Decision Models with Multiple Criteria is intended for the aware or enlightened practitioner, for anyone who uses decision or evaluation models---for research or for applications---and is willing to question his practice, to have a deeper understanding of what he does.The authors of this book are European academics working in four different universities and research institutions. They teach in engineering, mathematics, computer science and psychology schools. Their background is quite varied: mathematics, economics, engineering, law and geology, but they are all active in decision support and more particularly in multiple criteria decision support. Preference modelling, fuzzy logic, aggregation techniques, social choice theory, artificial intelligence, problem structuring, measurement theory and Operational Research are among their special interests.The authors are active in theoretical research on the foundations of decision aiding, mainly from an axiomatic point of view. Moreover, all the authors have been involved and continue to be engaged in a wide range of applications from software evaluation to location of a nuclear repository, through the rehabilitation of a sewer network or the location of high-voltage lines.

Table of Contents

Introduction	1	(18)
Motivations	1	(3)
What have we learned in the first volume?	4	(2)
Stepping stones for the analyst	6	(10)
Structure	7	(1)
Outline of the chapters	8	(1)
Chapter 2	8	(2)
Chapter 3	10	(1)
Chapter 4	11	(1)
Chapter 5	12	(1)
Chapter 6	13	(2)
Chapter 7	15	(1)
Intended audience	16	(1)
Who are the authors?	17	(1)
Conventions	17	(1)
Acknowledgements	18	(1)
Problem formulation and structuring	19	(48)
Decision Aiding Approaches	21	(7)
Decision Processes and Decision Aiding Processes	28	(6)
A descriptive model of the decision process	30	(2)
Decision Making and Decision Aiding	32	(2)
A model of the Decision Aiding Process	34	(12)
The Problem Situation	35	(2)
Problem Formulation	37	(4)
Evaluation Model	41	(3)
Final Recommendation	44	(2)
Problem structuring	46	(15)
Problem Structuring Methods	46	(1)
Cognitive Mapping	46	(1)
Strategic Choice	47	(1)
Soft Systems Methodology	48	(1)
Valued Focussed Thinking	49	(2)
Integrating Approaches	51	(1)
Discussion	52	(1)
Representing the problem situation	52	(2)
Formulating a problem	54	(2)
Constructing the Evaluation Model	56	(4)
Constructing the final recommendation	60	(1)
Update and Revision: an open problem	61	(2)
Conclusion	63	(4)
Numbers and preferences	67	(50)
Introduction	67	(1)
Numbers	67	(2)
Four basic examples	69	(7)
The race	69	(2)
The weather	71	(2)
The race again	73	(2)
The expert's advice	75	(1)
Evaluation and meaningfulness	76	(3)
Definitions	76	(2)
Comments	78	(1)
Stepping stones for this chapter	79	(1)
Numbers and preference relations	80	(3)
The comparison problem	81	(1)
The numerical representation problem	82	(1)
Content of the following sections	82	(1)
The comparison problem	83	(21)
Pointwise evaluations on an ordinal scale	83	(1)
Pure ordinal scale	83	(2)
Ordinal scale with a threshold	85	(2)
Ordinal scale with two thresholds	87	(2)
Ordinal scale with k thresholds	89	(1)
Ordinal scale with a degree of preference	90	(2)
Pointwise evaluations on an interval scale	92	(1)
Pure interval scale	92	(2)
Interval scale with a threshold	94	(1)
Pointwise evaluations on a ratio scale	95	(1)
Pure ratio scale	96	(1)
Interval evaluations on an ordinal scale	97	(1)
Pure ordinal scale	98	(2)
Ordinal scale with a threshold	100	(2)
Interval evaluations on an interval scale	102	(1)
Pure interval scale	102	(1)
Interval scale with a threshold	103	(1)
Summary of the comparison problem	103	(1)
The numerical representation problem	104	(10)
Weak order	104	(2)
Semiorder	106	(5)
Interval order	111	(2)
(P, Q, I)-structure	113	(1)
Valued preference relation	113	(1)
Conclusion	114	(1)
Appendix: binary relations and ordered sets	115	(2)
Aggregation---Overture	117	(52)
Introduction	117	(4)
How can this help the analyst?	119	(1)
Organisation of chapters 4--6	120	(1)
Social choice and MCDA	121	(6)
Aggregation functions	121	(2)
An example: the Borda method	123	(1)
Axioms and characterisation	123	(1)
Usefulness of the characterisation	124	(2)
Specificity of this approach	126	(1)
Conjoint measurement and MCDA	127	(20)
Additive value function	128	(1)
Showing tradeoffs	129	(1)
Conjoint Measurement	130	(1)
Uniqueness issues	131	(2)
Relevance of conjoint measurement results for MCDA	133	(1)
Marginal preferences within the additive value model	133	(2)
Leaning on the additive value model to elicit preferences	135	(5)
Tradeoffs or substitution rates	140	(2)
The measurement of global preference differences	142	(2)
Insufficiency of classical conjoint measurement	144	(1)
Flexible CSP	144	(1)
Non-transitive preferences	145	(1)
Promethee II	145	(2)
Conclusion	147	(1)
Parameters	147	(9)
Direct rating	148	(1)
Simos' cards method	149	(1)
Ranking the criteria	150	(1)
Analytic Hierarchy Process (AHP)	151	(1)
A classical technique in MAVT	151	(2)
General approach	153	(1)
Laplace's principle	154	(2)
Methods	156	(11)
AHP	157	(1)
The method	157	(1)
Some pointers	158	(1)
Electre I	159	(1)
The method	159	(1)
Some pointers	160	(1)
Electre III	161	(1)
The method	161	(1)
Some pointers	162	(1)
MAVT	162	(1)
The method	162	(1)
Some pointers	163	(1)
Promethee II	163	(1)
The method	163	(2)
Some pointers	165	(1)
Tactic	165	(1)
The method	165	(1)
Some pointers	166	(1)
Limitations of the axiomatic approach	167	(2)
Aggregation procedures	169	(68)
Aggregation functions	169	(1)
Aggregation of preference relations	170	(22)
The simple majority or Condorcet method	171	(1)
Axioms and characterisation	171	(2)
Discussion	173	(1)
When simple majority fails	174	(2)
Condorcet and TACTIC	176	(1)
What do we do with a non-transitive relation?	177	(1)
Weighted simple majority	178	(1)
Axioms and characterisation	178	(2)
Discussion	180	(1)
Cyclical preferences	180	(1)
Choosing the weights	180	(2)
Tactic and Condorcet	182	(1)
Absolute and qualified majorities	183	(1)
Axioms and characterisation	183	(1)
Discussion	184	(1)
Cyclical preferences	185	(1)
Choosing the concordance threshold	185	(2)
The qualified majority and ELECTRE I	187	(1)
The lexicographic method	188	(2)
Axioms and characterisation	190	(1)
Discussion	190	(2)
Aggregation of fuzzy relations	192	(10)
Construction of fuzzy preference relations	193	(1)
The Generalised Borda method	194	(1)
Axioms and characterisation	195	(1)
Discussion	196	(1)
Generalised Borda and Promethee II	196	(1)
The Generalised Condorcet method	197	(1)
Does it make sense to add the valuations?	198	(1)
Other possible extensions	198	(1)
Transitivity	199	(1)
Electre III	199	(1)
Pairwise aggregation into a fuzzy relation	199	(1)
General comment on the aggregation into a fuzzy relation	200	(2)
The difficulty of aggregating fuzzy relations	202	(1)
Aggregation of a performance table	202	(22)
Notations and definitions	203	(2)
A comment about commensurability	205	(2)
The min	207	(1)
Axioms and characterisation	207	(1)
Discussion	208	(1)
The weighted sum	209	(1)
Axioms and characterisation	209	(1)
Discussion	210	(2)
Choosing the weights	212	(2)
The leximin and leximax	214	(1)
Axioms and characterisation	215	(1)
Discussion	216	(2)
The outranking procedures	218	(3)
Discussion	221	(2)
The outranking procedures and Electre I	223	(1)
Aggregation of a linguistic performance table	224	(1)
Choice functions	225	(2)
Adapting the axioms to the choice problem	226	(1)
Aggregation of performances into a performance	227	(10)
Notation	229	(1)
The arithmetic mean	229	(1)
Axioms and characterisation	230	(3)
Discussion	233	(1)
Quasi-arithmetic means	233	(1)
Min, max and the other order statistics	234	(1)
Weighted mean, weighted sum	234	(3)
Multi-dimensional preference models	237	(90)
The additive value model	238	(16)
Independence and marginal preferences	238	(3)
The additive value model in the ``rich'' case	241	(1)
The case of two dimensions	241	(6)
The case of more than two dimensions	247	(3)
Standard sequences and beyond	250	(1)
The additive value model in the ``finite'' case	251	(3)
Models based on marginal traces	254	(19)
Decomposable preferences	255	(1)
Eliciting the general decomposable model	256	(2)
Non-strict decomposable model	258	(1)
The non-strict decomposable model	258	(1)
Eliciting the non-strict decomposable model	259	(1)
Insufficiency of the decomposable model	259	(2)
Insufficiency of marginal analysis: marginal traces	261	(2)
Generalising decomposable models using marginal traces	263	(4)
Models using marginal traces	267	(1)
Respect of the dominance relation	268	(2)
Properties of marginal preferences	270	(1)
Separability and independence	271	(1)
The case of weak orders	271	(1)
Eliciting the variants	272	(1)
Models based on marginal traces on differences	273	(30)
The additive difference model	273	(2)
Comparison of preference differences	275	(1)
A general family of models using traces on differences	276	(4)
Eliciting models using traces on differences	280	(1)
Testing	281	(1)
Models distinguishing three classes of differences	282	(1)
Simple majority or the Condorcet method	283	(1)
Weighted simple majority	284	(1)
Weighted qualified majority	284	(5)
Lexicographic preference relations	289	(1)
Other forms of weighted qualified majority	290	(3)
Examples of models using vetoes	293	(2)
Weighted qualified majority with veto	295	(1)
Weighted relative majority: threshold and veto	296	(2)
Models distinguishing five classes of differences	298	(3)
Models distinguishing many classes of differences	301	(2)
Models using both traces	303	(8)
Marginal traces and traces on differences	304	(2)
Eliciting models using both kinds of traces	306	(1)
Procedure	306	(3)
Elicitation	309	(1)
Models distinguishing five classes of differences	310	(1)
The weighted majority model revisited	310	(1)
Other models	311	(1)
Weakly differentiated preference differences	311	(7)
Concordance relations	312	(1)
The importance relation	313	(1)
Preference relations on attributes	314	(2)
Relationship with actual outranking methods	316	(1)
Elicitation issues	317	(1)
Models for valued preferences	318	(4)
The measurement of preference differences	319	(1)
Fuzzy preference relations	320	(2)
Social choice vs. Conjoint measurement	322	(5)
Making recommendation	327	(72)
Introduction	327	(5)
Position of the problem	327	(1)
What kind of recommendation?	328	(1)
Choosing	329	(1)
Ranking	329	(1)
Sorting	330	(2)
Using a value function	332	(5)
Relative evaluation	333	(1)
Choosing	333	(1)
Ranking	334	(1)
Absolute evaluation: Sorting	335	(1)
Limiting profiles	335	(1)
Prototypes	336	(1)
Using several value functions	337	(18)
Linear programming assessment	337	(1)
Beyond standard sequences	338	(2)
Linear Programming assessment techniques	340	(2)
Variants of LP based assessment	342	(1)
UTA	342	(2)
MACBETH	344	(3)
Choosing with a set of additive value functions	347	(1)
Ranking with a set of additive value functions	348	(1)
Sorting with a set of additive value functions	348	(1)
Example: Thierry's choice	349	(1)
Thierry's choice	349	(2)
Using UTA	351	(1)
Choosing	352	(1)
Ranking	353	(1)
Sorting	353	(2)
Other preference models	355	(30)
The extent of the problem	355	(1)
Simple majority	355	(1)
Electre I	356	(1)
Electre III	357	(1)
How things may go wrong: examples	358	(3)
Choice procedures	361	(1)
Crisp relations	362	(1)
Procedures based on covering relations	363	(2)
Procedures based on kernels	365	(3)
Other procedures	368	(1)
Valued relations	368	(1)
Use of λ-cuts	369	(1)
Fuzzyfication of crisp procedures	369	(1)
Procedures based on scores	370	(1)
Examples	371	(1)
Ranking procedures	372	(1)
Crisp relations	372	(1)
Using the transitive closure	373	(3)
Copeland scores	376	(1)
Ranking by repeated choice	377	(2)
Use of distances	379	(1)
Valued relations	380	(1)
Sorting procedures	380	(1)
An overview of Electre Tri	381	(3)
Implementation of Electre Tri	384	(1)
Robustness of the conclusions	385	(14)
Introduction	385	(1)
Robustness versus stability	386	(1)
Alternative definitions of robustness in the literature	386	(2)
Robustness illustrated: examples	388	(7)
Robust methods	395	(1)
Back to Thierry's choice	395	(1)
Robustness and MCDA	396	(1)
Summary and open questions	397	(2)
Conclusion	399	(10)
Did we keep our promise?	399	(2)
Decision Aiding Methodology	401	(2)
Decision aiding approaches and tools	403	(1)
Preference modelling	403	(1)
Preference aggregation	404	(2)
Final stepping stones	406	(1)
And after all this?	407	(2)
Bibliography	409	(24)
Name Index	433	(6)
Subject Index	439