1 We wish to thank Jose Figueira and Marc Pirlot for their helpful comments on an earlier draft o... more 1 We wish to thank Jose Figueira and Marc Pirlot for their helpful comments on an earlier draft of this text. Our greatest debt is to Salvatore Greco, Benedetto Matarazzo and Roman S lowiński who alerted us on the relation between our results on noncompensatory sorting models and the results in S lowiński et al. on sorting models using a Sugeno integral. Furthermore, their detailed comments have much contributed to improve an earlier version of this text. The usual caveat clearly applies.
1 We wish to thank Jose Figueira and Marc Pirlot for their comments on an earlier draft of this t... more 1 We wish to thank Jose Figueira and Marc Pirlot for their comments on an earlier draft of this text. Our greatest debt is to Salvatore Greco, Benedetto Matarazzo and Roman S lowiński who alerted us on the relation between our results on noncompensatory sorting models and the results in S lowiński et al. on sorting models using a Sugeno integral. Furthermore, their detailed comments have much contributed to improve an earlier version of this text. The usual caveat clearly applies.
In this paper we study a particular method that builds a partial ranking on the basis of a valued... more In this paper we study a particular method that builds a partial ranking on the basis of a valued preference relation. This method which is used in the MCDM method PROMETHEE I, is based on "leaving" and "entering" flows. We show that this method is characterized by a system of three independent axioms.
1 We wish to thank M. Abdellaoui, J.-P. Doignon, Ch. Gonzales, Th. Marchant, P.P. Wakker and an a... more 1 We wish to thank M. Abdellaoui, J.-P. Doignon, Ch. Gonzales, Th. Marchant, P.P. Wakker and an anonymous referee for their very helpful suggestions and comments on earlier drafts of this text. The usual caveat applies. Denis Bouyssou gratefully acknowledges the support of the Centre de Recherche de l'ESSEC and the Brussels-Capital Region through a "Research in Brussels" action grant.
A general model is presented which encompasses manyprocedures used for aggregating preferences in... more A general model is presented which encompasses manyprocedures used for aggregating preferences in multicriteria decisionmaking (or decision aid) methods. Are covered in particular: MAUT,ELECTRE and several other outranking methods. The main interestof the model is to provide a key for understanding the differences betweenmethods. Methods are analyzed in terms of their way of dealingwith "preference differences" on each criterion/attribute. The
Based on a general framework for conjoint measurement that allows for intransitive preferences, t... more 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.
The notion of concordance is central to many multiple criteria techniques relying on ordinal info... more The notion of concordance is central to many multiple criteria techniques relying on ordinal information, e.g. outranking methods. It leads to compare alternatives by pairs on the basis of a comparison of coalitions of attributes in terms of "importance". This paper proposes a characterization of the binary relations that can be obtained using such comparisons, within a general framework for conjoint measurement that allows for intransitive preferences. We show that such relations are mainly characterized by the very rough differentiation of preference differences that they induce on each attribute.
This paper studies conjoint measurement models tolerating intransitivities that closely resemble ... more 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.
This paper analyzes conjoint measurement models allowing for intransitive and/or incomplete prefe... more 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.
Outranking relations are most often built using a concordance-discordance principle. Such relatio... more Outranking relations are most often built using a concordance-discordance principle. Such relations are in general neither transitive nor complete. This is not to say that the concordance-discordance principle does not impose some 'structural' restrictions on these relations. We show why this question may be of some importance for analysing the various techniques designed to build a recommendation on the basis of such relations. These restrictions are studied for the ELECTRE and PROMETHEE methods.
1 We wish to thank Jose Figueira and Marc Pirlot for their helpful comments on an earlier draft o... more 1 We wish to thank Jose Figueira and Marc Pirlot for their helpful comments on an earlier draft of this text. Our greatest debt is to Salvatore Greco, Benedetto Matarazzo and Roman S lowiński who alerted us on the relation between our results on noncompensatory sorting models and the results in S lowiński et al. on sorting models using a Sugeno integral. Furthermore, their detailed comments have much contributed to improve an earlier version of this text. The usual caveat clearly applies.
1 We wish to thank Jose Figueira and Marc Pirlot for their comments on an earlier draft of this t... more 1 We wish to thank Jose Figueira and Marc Pirlot for their comments on an earlier draft of this text. Our greatest debt is to Salvatore Greco, Benedetto Matarazzo and Roman S lowiński who alerted us on the relation between our results on noncompensatory sorting models and the results in S lowiński et al. on sorting models using a Sugeno integral. Furthermore, their detailed comments have much contributed to improve an earlier version of this text. The usual caveat clearly applies.
In this paper we study a particular method that builds a partial ranking on the basis of a valued... more In this paper we study a particular method that builds a partial ranking on the basis of a valued preference relation. This method which is used in the MCDM method PROMETHEE I, is based on "leaving" and "entering" flows. We show that this method is characterized by a system of three independent axioms.
1 We wish to thank M. Abdellaoui, J.-P. Doignon, Ch. Gonzales, Th. Marchant, P.P. Wakker and an a... more 1 We wish to thank M. Abdellaoui, J.-P. Doignon, Ch. Gonzales, Th. Marchant, P.P. Wakker and an anonymous referee for their very helpful suggestions and comments on earlier drafts of this text. The usual caveat applies. Denis Bouyssou gratefully acknowledges the support of the Centre de Recherche de l'ESSEC and the Brussels-Capital Region through a "Research in Brussels" action grant.
A general model is presented which encompasses manyprocedures used for aggregating preferences in... more A general model is presented which encompasses manyprocedures used for aggregating preferences in multicriteria decisionmaking (or decision aid) methods. Are covered in particular: MAUT,ELECTRE and several other outranking methods. The main interestof the model is to provide a key for understanding the differences betweenmethods. Methods are analyzed in terms of their way of dealingwith "preference differences" on each criterion/attribute. The
Based on a general framework for conjoint measurement that allows for intransitive preferences, t... more 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.
The notion of concordance is central to many multiple criteria techniques relying on ordinal info... more The notion of concordance is central to many multiple criteria techniques relying on ordinal information, e.g. outranking methods. It leads to compare alternatives by pairs on the basis of a comparison of coalitions of attributes in terms of "importance". This paper proposes a characterization of the binary relations that can be obtained using such comparisons, within a general framework for conjoint measurement that allows for intransitive preferences. We show that such relations are mainly characterized by the very rough differentiation of preference differences that they induce on each attribute.
This paper studies conjoint measurement models tolerating intransitivities that closely resemble ... more 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.
This paper analyzes conjoint measurement models allowing for intransitive and/or incomplete prefe... more 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.
Outranking relations are most often built using a concordance-discordance principle. Such relatio... more Outranking relations are most often built using a concordance-discordance principle. Such relations are in general neither transitive nor complete. This is not to say that the concordance-discordance principle does not impose some 'structural' restrictions on these relations. We show why this question may be of some importance for analysing the various techniques designed to build a recommendation on the basis of such relations. These restrictions are studied for the ELECTRE and PROMETHEE methods.
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