Modeling attitudes toward uncertainty through the use of the Sugeno integral

The aim of the paper is to present under uncertainty, and in an ordinal framework, an axiomatic treatment of the Sugeno integral in terms of preferences which parallels some earlier derivations devoted to the Choquet integral. Some emphasis is given to the characterization of uncertainty aversion.Sugeno integral; uncertainty aversion; preference relations; ordinal information

Imprecise linear filtering: a second step

International audienceLinear digital signal processing consists in convo- luting the input sampled signal with the discrete version of the impulse response of a filter designed by an expert. More than often, a unique impulse re- sponse does not represent the complete knowledge of the expert who should have proposed more than one appropriate filter. In a recent paper, we have proposed an extension of the finite impulse response filtering that able to represent the fact that the fil- ter is imprecisely known. This extension leads to compute an interval-valued filtered signal. In this paper, we propose a natural follow-up of this work by considering interval-valued input signals and re- placing the Choquet integral by the Šipoš integral

Modeling attitudes toward uncertainty through the use of the Sugeno integral

International audienceThe aim of the paper is to present under uncertainty, and in an ordinal framework, an axiomatic treatment of the Sugeno integral in terms of preferences which parallels some earlier derivations devoted to the Choquet integral. Some emphasis is given to the characterization of uncertainty aversion

Capacités qualitatives et information incomplète

International audienceCet article étudie les capacités qualitatives, qui sont des fonctions d'ensemble monotones croissantes à valeurs sur un ensemble totalement ordonné muni d'une fonction de renversement de l'ordre. En nous inspirant du rôle joué par les probabilités pour les capacités quantitatives, nous cherchons à savoir si les capacités qualitatives peuvent être considérées comme des ensembles de mesures de possibilité. Plus précisément nous montrons que toute capacité qualitative est caracterisée par une classe de mesures de possibilité. De plus, les bornes inférieures de cette classe sont suffisantes pour reconstruire la capacité et leur nombre caractérise sa complexité. Nous présentons aussi un axiome généralisant la maxitivité des mesures de possibilité qui revient à préciser le nombre de mesures de possibilité nécessaires à la reconstruction de la capacité. Cet axiome nous permet aussi d'établir un lien entre capacité qualitative et logique modale non regulière. Enfin nous donnons quelques résultats pour caractériser la quantité d'information contenue dans une capacité

Preference modelling on totally ordered sets by the Sugeno integral

International audienceWe present in this paper necessary and sufficient conditions for the representation of preferences in a decision making problem, by the Sugeno integral, in a purely ordinal framework. We distinguish between strong and weak representations

Preference modelling on totally ordered sets by the Sugeno integral

We present in this paper necessary and sufficient conditions for the representation of preferences in a decision making problem, by the Sugeno integral, in a purely ordinal framework. We distinguish between strong and weak representations.Preference representation; Sugeno integral; Ordinal information

The logical encoding of Sugeno integrals

International audienceSugeno integrals are a well-known family of qualitative multiple criteria aggregation operators. The paper investigates how the behavior of these operators can be described in a prioritized propositional logic language, namely possibilistic logic. The case of binary-valued criteria, which amounts to providing a logical description of the fuzzy measure underlying the integral, is first considered. The general case of a Sugeno integral when criteria are valued on a discrete scale is then studied

Sugeno integral in a finite Boolean algebra

International audienceThe aim of this paper is to provide a representation theorem of the Sugeno integral when the evaluation scale is a finite Boolean algebra. This result is a generalisation of a result proved when the evaluation scale is totally ordered. A major difficulty is the renunciation of the comonotonic functions which have to be replaced by the co-included functions. So we need to care about the properties satisfied by the Sugeno integral when the evaluation scale is a finite totally ordered set. To begin we show that, when the scale is totally ordered, the co-included functions are solely needed to characterise the Sugeno integral and that they are less constraining than the comonotonic functions classically used. Next we focus on finite Boolean algebra, and in this new context we define the Sugeno integral and we present the properties still satisfied. To end this article, we present a representation theorem of the Sugeno integral on a finite Boolean algebra

Imprecise Expectations for Imprecise Linear Filtering

In the last 10 years, there has been increasing interest in interval valued data in signal processing. According to the conventional view, an interval value supposedly reflects the variability of the observation process. Generally, the considered variability is associated with either random noise or the uncertainty that underlies the observation process. In most sensor measure based applications, the raw sensor signal has to be processed by an appropriate filter to increase the signal to noise ratio or simply to recover the signal to be measured. In both cases, the output filter is obtained by convoluting the sensor signal with a supposedly known appropriate impulse response. However, in many real life situations, this impulse response cannot be precisely specified. The filtered value can thus be considered as biased by this arbitrary choice of one impulse response among all possible impulse responses considered in this specific context. In this paper, we propose a new approach to perform filtering that aims at computing an interval-valued signal that contains all outputs of filtering processes involving a coherent family of conventional linear filters. This approach is based on a very straightforward extension of the expectation operator involving appropriate concave capacities

Extension signée de la domination des noyaux maxitifs

International audienceLes noyaux de convolutions sont des outils indispensables en traitement du signal. Ils permettent de modéliser le comportement d'un capteur, de définir les propriétés d'un filtre, de transformer une opération continue en opération discrète, etc. Une des difficultés est cependant d'identifier quel noyau utiliser pour quelle application. Dans des articles précédents, nous nous sommes appuyés sur une analogie simple entre noyaux de convolution positifs et distributions de probabilités pour définir la notion de noyau maxitif. Un noyau maxitif permet de représenter un ensemble convexe de noyaux de convolutions positifs, c'est à dire une information imprécise sur le noyau à utiliser. Cependant, dans de nombreuses applications, comme par exemple le filtrage, on peut être amené à utiliser des noyaux de convolutions signés. Nous proposons, dans cet article, d'étendre la notion de domination des noyaux maxitifs aux noyaux de convolution signés, ce qui va nous mener dans la contrée controversée des fonctions d'ensembles signées donc non-monotones