Résumé: This talks presents to what extent the classification in terms of belief function and upper/lower probabilities carries over to qualitative fuzzy measures and possibility theory.

Résumé: Cet article présente des variantes de l’intégrale de Sugeno dans un cadre qualitatif fini. On introduit tout d’abord trois facons d’interpréter les poids d’importance associés aux groupes de critères, sur une algèbre de Heyting. On introduit ensuite l’idée de “désintégrale”, duale de celle d’intégrale. Lors de l’évaluation d’un objet, une désintégrale est maximale si aucun défaut eventuel n’est présenté de manière notable, tandis qu’une intégrale est maximale si tous les avantages eventuels sont suffisamment présents. Cette idée conduit à une représentation bipolaire des préférences, au moyen d’une paire constituée par une intégrale et une désintégrale.

Résumé: This paper presents several variants of Sugeno integral, and in particular the idea of (qualitative) desintegrals, a dual of integrals. When evaluating an item, desintegrals are maximal if no defects at all are present, while integrals are maximal if all advantages are sufficiently present. This idea leads to a bipolar representation of preferences, by means of a pair made of an integral and a desintegral, whose possibilistic logic counterparts are outlined (in the case where criteria are binary).

Résumé: Deconvolution consists of reconstructing a signal from blurred (and usuall noisy) sensory observations. It requires perfect knowledge of the impulse response of the sensor. Relevant works in the litterature propose methods with improved precision and robustness. But those methods are not able to account for a partial knowledge of the impulse response of the sensor. In this article, we experimentally show that inverting a Choquet capacity-based model of an imprecise knowledge of this impulse response allows to robustly recover the measured signal. The method we use is an interval valued extension of the well known Schultz procedure.

Résumé: Integrals are currently used in multiple criteria analysis for synthesizing into a global evaluation the advantages possessed by a potential choice. As such, integrals are operators that increase with the criteria evaluations. However, an item may be also evaluated in terms of its defects. Then the more and the greater the defects, the smaller the evaluation should be. An operator that can provide a synthesis of the defects of an item in this sense is called a desintegral. Desintegrals are maximal when no defects at all are present, while integrals are maximal when all advantages are sufficiently present. So, the greater the value of an integral, or a desintegral, the better the corresponding item since advantages are greater, or defects are smaller respectively. Desintegrals implicitly refer to a negative scale, since an order-reversing mapping of the scale used for evaluating each criterion transforms the degree to which the value is advantageous into a degree to which it is disadvantageous, and conversely. In this paper, we provide an organised description of counterparts to Sugeno integrals that synthesize positive or negative evaluations in the qualitative framework of a totally ordered residuated lattice equipped with an involutive negation. We exploit three kinds of criteria weighting schemes that are allowed by this algebraic structure.