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42
An Axiomatic Approach to Noncompensatory Sorting Methods In MCDM, I: The case of two categories
, 2004
"... In the literature on MCDM, many methods have been proposed in order to sort alternatives evaluated on several attributes into ordered categories. Most of them were proposed on an ad hoc basis. Using tools from conjoint measurement, this paper takes a more theoretical approach to these sorting method ..."
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Cited by 42 (22 self)
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In the literature on MCDM, many methods have been proposed in order to sort alternatives evaluated on several attributes into ordered categories. Most of them were proposed on an ad hoc basis. Using tools from conjoint measurement, this paper takes a more theoretical approach to these sorting methods. We provide an axiomatic analysis of the partitions of alternatives into two categories that can be obtained using what we call "noncompensatory sorting models". These models have strong links with the pessimistic version of ELECTRE TRI and our analysis allows to pinpoint what appears to be the main distinctive features of ELECTRE TRI when compared to other sorting methods.
Preferences for multiattributed alternatives: Traces, Dominance, and Numerical Representations
 JOURNAL OF MATHEMATICAL PSYCHOLOGY
, 2002
"... This paper analyzes conjoint measurement models allowing for intransitive and/or incomplete preferences. This analysis is based on the study of marginal traces induced on coordinates by the preference relation and uses conditions guaranteeing that these marginal traces are complete. Within the ..."
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Cited by 35 (18 self)
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This paper analyzes conjoint measurement models allowing for intransitive and/or incomplete preferences. This analysis is based on the study of marginal traces induced on coordinates by the preference relation and uses conditions guaranteeing that these marginal traces are complete. Within the
'Additive Difference' Models Without Additivity and Subtractivity
"... This paper studies conjoint measurement models tolerating intransitivities that closely resemble Tversky's additive difference model while replacing additivity and subtractivity by mere decomposability requirements. We offer a complete axiomatic characterization of these models without having r ..."
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Cited by 27 (22 self)
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This paper studies conjoint measurement models tolerating intransitivities that closely resemble Tversky's additive difference model while replacing additivity and subtractivity by mere decomposability requirements. We offer a complete axiomatic characterization of these models without having recourse to unnecessary structural assumptions on the set of objects. This shows the pure consequences of several cancellation conditions that have often be used in the analysis of more traditional conjoint measurement models. Our conjoint measurement models contain as particular cases most aggregation rules that have been proposed in the literature.
From decision theory to decision aiding methodology (my very personal version of this history and some related reflections)
, 2003
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A characterization of strict concordance relations
, 2001
"... Based on a general framework for conjoint measurement that allows for intransitive preferences, this paper proposes a characterization of “strict concordance relations”. This characterization shows that the originality of such relations lies in their very crude way to distinguish various levels of “ ..."
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Cited by 21 (16 self)
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Based on a general framework for conjoint measurement that allows for intransitive preferences, this paper proposes a characterization of “strict concordance relations”. This characterization shows that the originality of such relations lies in their very crude way to distinguish various levels of “preference differences” on each attribute.
Preference modelling
 State of the Art in Multiple Criteria Decision Analysis
, 2005
"... This paper provides the reader with a presentation of preference modelling fundamental notions as well as some recent results in this field. Preference modelling is an inevitable step in a variety of fields: economy, sociology, psychology, mathematical programming, even medicine, archaeology, and ob ..."
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Cited by 18 (1 self)
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This paper provides the reader with a presentation of preference modelling fundamental notions as well as some recent results in this field. Preference modelling is an inevitable step in a variety of fields: economy, sociology, psychology, mathematical programming, even medicine, archaeology, and obviously decision analysis. Our notation and some basic definitions, such as those of binary relation, properties and ordered sets, are presented at the beginning of the paper. We start by discussing different reasons for constructing a model or preference. We then go through a number of issues that influence the construction of preference models. Different formalisations besides classical logic such as fuzzy sets and nonclassical logics become necessary. We then present different types of preference structures reflecting the behavior of a decisionmaker: classical, extended and valued ones. It is relevant to have a numerical representation of preferences: functional representations, value functions. The concepts of thresholds and minimal representation are also introduced in this section. In section 7, we briefly explore the concept of deontic logic (logic of preference) and other formalisms associated with &quot;compact representation of preferences &quot; introduced for special purposes. We end the paper with some concluding remarks.
DECISION RULE APPROACH
"... We present the methodology of MultipleCriteria Decision Aiding (MCDA) based on preference modelling in terms of “if…, then … ” decision rules. The basic assumption of the decision rule approach is that the decision maker (DM) accepts to give preferential information in terms of examples of decisi ..."
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Cited by 18 (9 self)
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We present the methodology of MultipleCriteria Decision Aiding (MCDA) based on preference modelling in terms of “if…, then … ” decision rules. The basic assumption of the decision rule approach is that the decision maker (DM) accepts to give preferential information in terms of examples of decisions and looks for simple rules justifying her decisions. An important advantage of this approach is the possibility of handling inconsistencies in the preferential information, resulting from hesitations of the DM. The proposed methodology is based on the elementary, natural and rational principle of dominance. It says that if action is at least as good as action on each criterion from a considered family, then is also comprehensively at least as good as The set of decision rules constituting the preference model is induced from the preferential information using a knowledge discovery technique properly modified, so as to handle the dominance principle. The mathematical basis of the decision rule approach to MCDA is the Dominancebased Rough Set Approach (DRSA) developed by the authors. We present some basic applications of this approach, along with didactic examples whose aim is to show in an easy way how DRSA can be used in various contexts of MCDA.
Conjoint Measurement without additivity and transitivity
 In N. Meskens & M. Roubens (Eds.), Advances in decision analysis
, 1999
"... this paper may be seen both as a generalisation of (2) dropping transitivity and completeness and as a generalisation of (4) dropping additivity. In their most general form they are of the type (see also Goldstein (1991)): b # F(p 1 (a 1 , b 1 ), p 2 (a 2 , b 2 ), ..., p )) # 0 (5) where F ..."
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Cited by 13 (8 self)
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this paper may be seen both as a generalisation of (2) dropping transitivity and completeness and as a generalisation of (4) dropping additivity. In their most general form they are of the type (see also Goldstein (1991)): b # F(p 1 (a 1 , b 1 ), p 2 (a 2 , b 2 ), ..., p )) # 0 (5) where F is non decreasing in all its arguments. This type of non transitive decomposable conjoint models may seem exceedingly general. However we shall see that this model and its specialisations: . imply substantive requirements on #, . may be axiomatised in a simple way avoiding the use of a denumerable number of conditions in the finite case and of unnecessary structural assumptions in the infinite case, . allow to study the "pure consequences" of cancellation conditions in the absence of transitivity, completeness and structural requirements on X, . are sufficiently general to include as particular cases many aggregation rules that have been proposed in the literature. II. Outline of Results In this section we give, without proof, a number of sample results concerning model (5) and show how they can be used. Let be a binary relation on a set X = X . This relation is said to satisfy: # # # # # # # # # # #         , ) , ( ) , ( or ) , ( ) , ( ) , ( ) , ( and ) , ( ) , ( i i i i i i i i i i i i i b w a z d y c x d w c z b y a x # # # # for all x i , y i , z i , w i # X i and all a i , b i , c i , d i # X i , with X i = X j j # i # . We say that satisfies RC if it satisfies RC i for i = 1, 2,..., n. Condition RC (inteRattribute Cancellation) suggests that # induces on X i a relation that compares "preference differences" in a wellbehaved way: if (x i , y i ) is a "larger preference difference" than (z i , w i ) then if (z i , c i ) (w i , d ...