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On the stability of outranking relations : Theoretical and practical aspects

Abstract : Using a multicriteria decision aid method to provide a recommendation requires the determination of numerous parameters. These parameters are obtained during a preference elicitation process, to construct an evaluation model that summarises the subjective aspects related to the decision-maker's perceptions or expectations, as for example the criteria weights, which appreciate the local role of each criterion in the construction of the overall evaluations. Two different approaches exist to specify theses values : - either via direct preference information, where the values are first assessed and then the overall evaluations are computed, or - via indirect preference information, where some a priori partial knowledge about the resulting evaluation model is used in order to infer plausible estimators of the parameters. However, determining precisely the numerical values of these parameters is an important issue: As the final recommendation is highly depending on these parameters, it is of the highest importance to avoid impreciseness or to be able to measure their impact on the modeling of the preferences. In addition, when considering an indirect elicitation of these parameters, according to an incomplete knowledge of the resulting evaluation model, the selection of one particular set of compatible parameters is also a very debatable question. The work we present in this thesis takes part within the multicriteria decision aid methods, more specifically within the outranking philosophy. It focuses on the stability concept, which characterises the impact of some possible impreciseness of the criteria weights on the evaluation model. According to a given vector of weights w, a positive (resp. negative) outranking statement is said to be stable if it only depends on the preorder of the weights, i.e. it is validated (resp. invalidated) for all vectors of weights having the same preorder than w. As it is easier for a decision-maker to validate a preorder than a precise vector of weights, every stable statements can be considered as safer. By contrast, an unstable statement may be reversed by a slight tuning of the weights, highlighting a great weakness and the need to provide precise weights. The thesis is divided into three parts. The first one is a brief state of the art about the decision aid domain, that focuses on the preference elicitation processes and robustness concerns, in order to motivate our work. The second part focuses on the stability concept, to give a theoretical framework to our work, more precisely with the defining of mathematical models to elicit a vector of weights compatible with a set of preferential information. Last but not least, the third part of the thesis intends to implement these models on real practical cases.
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Thomas Veneziano. On the stability of outranking relations : Theoretical and practical aspects. Discrete Mathematics [cs.DM]. Télécom Bretagne, Université de Bretagne-Sud, 2012. English. ⟨tel-00801801⟩

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