Résumé: Le magazine “L’Etudiant” a publié en septembre 2012 un classement des “villes où il fait bon étudier”, présentant un palmarès multi-critère des 41 villes françaises de plus de 8000 étudiants. Nous proposons ici une étude visant à analyser ce palmarès à travers des méthodes d’agrégation diversifiées, afin de faire ressortir les invariants d’un tel classement de villes, et au contraire des effets directement liés à l’utilisation de telle ou telle méthode.

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DOI: 10.1016/j.cor.2013.04.003
Résumé: We study in this paper the generation of the Choquet optimal solutions of biobjective combinatorial optimization problems. Choquet optimal solutions are solutions that optimize a Choquet integral. The Choquet integral is used as an aggregation function, presenting dierent parameters, and allowing to take into account the interactions between the objectives. We develop a new property that characterizes the Choquet optimal solutions. From this property, a general method to easily generate these solutions in the case of two objectives is dened. We apply the method to two classical biobjective optimization combinatorial optimization problems: the biobjective knapsack problem and the biobjective minimum spanning tree problem. We show that Choquet optimal solutions that are not weighted sum optimal solutions represent only a small proportion of the Choquet optimal solutions and are located in a specic area of the objective space, but are much harder to compute than weighted sum optimal solutions.

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Résumé: In machine learning, the multiple classifiers aggregation problems consist in using multiple classifiers to enhance the quality of a single classifier. Simple classifiers as mean or majority rules are already used, but the aggregation methods used in voting theory or multi-criteria decision making should increase the quality of the obtained results. Meanwhile, these methods should lead to better interpretable results for a human decision-maker. We present here the results of a first experiment based on the use of Choquet integral, decisive sets and rough sets based methods on four different datasets.

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Résumé: In the context of MultiCriteria Decision Aid, we present new properties of a 2-additive bi-capacity by using a bipolar M¨obius transform. We use these properties in the identification of a 2-additive bi-capacity when we represent a cardinal information by a Choquet integral with respect to a 2-additive bi-capacity.

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DOI: 10.1016/j.ejor.2012.10.013
Résumé: This paper aims at introducing and investigating a new family of merely qualitative models for multicriteria decision making. Such models do not require any numerical representation. Within this family, we will focus on decision rules using reference levels in order to help comparing several alternatives. We will investigate both the descriptive potential of such rules and their axiomatic foundations. After recalling the descriptive and prescriptive limitations of merely ordinal rules that do not use reference points, we will introduce a new axiom requiring that the Decision Maker's preference between two alternatives depends on the respective positions of their consequences relatively to reference levels. Under this assumption we will determine the only possible form for the decision rule and characterize some particular instances of this rule under transitivity constraints. Our results show that introducing reference points overcomes the usual limitations of purely ordinal aggregation methods, by moving the application point of Arrow's theorem.

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