Numerical Sensitivity and Efficiency in the Treatment of Epistemic and Aleatory Uncertainty

The treatment of both aleatory and epistemic uncertainty by recent methods often requires an high computational effort. In this abstract, we propose a numerical sampling method allowing to lighten the computational burden of treating the information by means of so-called fuzzy random variables

How to Handle Missing Values in Multi-Criteria Decision Aiding?

International audienceIt is often the case in the applications of Multi-Criteria Decision Making that the values of alternatives are unknown on some attributes. An interesting situation arises when the attributes having missing values are actually not relevant and shall thus be removed from the model. Given a model that has been elicited on the complete set of attributes, we are looking thus for a way-called restriction operator-to automatically remove the missing attributes from this model. Axiomatic characterizations are proposed for three classes of models. For general quantitative models, the restriction operator is characterized by linearity, recursivity and decomposition on variables. The second class is the set of monotone quantitative models satisfying normal-ization conditions. The linearity axiom is changed to fit with these conditions. Adding recursivity and symmetry, the restriction operator takes the form of a normalized average. For the last class of models-namely the Choquet integral, we obtain a simpler expression. Finally, a very intuitive interpretation is provided for this last model

Interval analysis on non-linear monotonic systems as an efficient tool to optimise fresh food packaging

IATE Axe 5 : Application intégrée de la connaissance, de l’information et des technologies permettant d’accroître la qualité et la sécurité des alimentsInternational audienceWhen few data or information are available, the validity of studies performing uncertainty analysis or robust design optimisation (i.e., parameter optimisation under uncertainty) with a probabilistic approach is questionable. This is particularly true in some agronomical fields, where parameter and variable uncertainties are often quantified by a handful of measurements or by expert opinions. In this paper, we propose a simple alternative approach based on interval analysis, which avoids the pitfalls of a classical probabilistic approach. We propose simple methods to achieve uncertainty propagation, parameter optimisation and sensitivity analysis in cases where the model satisfies some monotonic properties. As a real-world case study, we interest ourselves to the application developed in our laboratory that has motivated the present work, that is the design of sustainable food packaging preserving fresh fruits and vegetables as long as possible

Special Cases

International audienceThis chapter reviews special cases of lower previsions, that are instrumental in practical applications. We emphasize their various advantages and drawbacks, as well as the kind of problems in which they can be the most useful

Idempotent conjunctive combination of belief functions: Extending the minimum rule of possibility theory.

IATE : Axe 5 Application intégrée de la connaissance, de l’information et des technologies permettant d’accroître la qualité et la sécurité des aliments Contact : [email protected] (S. Destercke), [email protected] (D. Dubois) Fax: +33 0 4 9961 3076.International audienceWhen conjunctively merging two belief functions concerning a single variable but coming from different sources, Dempster rule of combination is justified only when information sources can be considered as independent. When dependencies between sources are ill-known, it is usual to require the property of idempotence for the merging of belief functions, as this property captures the possible redundancy of dependent sources. To study idempotent merging, different strategies can be followed. One strategy is to rely on idempotent rules used in either more general or more specific frameworks and to study, respectively, their particularisation or extension to belief functions. In this paper, we study the feasibility of extending the idempotent fusion rule of possibility theory (the minimum) to belief functions. We first investigate how comparisons of information content, in the form of inclusion and least-commitment, can be exploited to relate idempotent merging in possibility theory to evidence theory. We reach the conclusion that unless we accept the idea that the result of the fusion process can be a family of belief functions, such an extension is not always possible. As handling such families seems impractical, we then turn our attention to a more quantitative criterion and consider those combinations that maximise the expected cardinality of the joint belief functions, among the least committed ones, taking advantage of the fact that the expected cardinality of a belief function only depends on its contour function

Relating Imprecise Representations of imprecise Probabilities

International audienceThere exist many practical representations of probability families that make them easier to handle. Among them are random sets, possibility distributions, probability intervals, Ferson's p-boxes and Neumaier's clouds. Both for theoretical and practical considerations, it is important to know whether one representation has the same expressive power than other ones, or can be approximated by other ones. In this paper, we mainly study the relationships between the two latter representations and the three other ones

On the relationships between random sets, possibility distributions, p-boxes and clouds

There are many practical representations of probability families that make them easier to handle in applications. Among them are random sets, possibility distributions, Ferson's p-boxes and Neumaier's clouds. Both for theoretical and practical considerations, it is very useful to know whether one representation can be translated into or approximated by other ones. We first briefly recall formalisms and existing results, before exhibiting relationships between all these representations. In this note, which is a summary of an extended forthcoming paper, we restrict ourselves to representations on a finite set X

Aggregation of expert opinions and uncertainty theories

National audienceThe problem of expert opinions representation and aggregation has long been adressed in the only framework of probability theory. Nevertheless, recent years have witnessed many proposals in other uncertainty theories (possibility theory, evidence theory, imprecise probabilities). This paper casts the problem of aggregating expert opinions in a common underlying framework and shows how uncertainty theories fit into this framework. Differences between theories are then emphasized and discussed

Possibilistic information fusion using maximal coherent subsets (LFA 2007)

National audienceWhen multiple sources provide information about the same badly known quantity, aggregating them into a coherent and interpretable synthesis is often a tedious problem, especially when some conflict is present. In this paper, we propose and explore a fusion method using the notion of maximal coherent subsets (often used in logic) on quantitative possibility distributions. This methods result, a fuzzy belief structure, is then used to extract useful information about sources or to build a final synthetic possibility distribution.Lorsque plusieurs sources fournissent de l'information à propos d'une même quantité mal connue, en faire une synthèse cohérente et interprétable est souvent un problème difficile, surtout en présence de conflit entre les sources. Dans cet article, nous proposons et étudions une méthode de fusion basée sur la théorie des possibilités et sur la notion de sous-ensembles maximaux cohérents, une notion souvent utilisée dans le raisonnement logique. Cette méthode, dont le résultat final est une fonction de croyance floue, est ensuite utilisée aussi bien pour extraire de l'information utile sur les sources que pour construire une distribution synthétique finale