Monte Carlo and fuzzy interval propagation of hybrid uncertainties on a risk model for the design of a flood protection dike

International audienceA risk model may contain uncertainties that may be best represented by probability distributions and others by possibility distributions. In this paper, a computational framework that jointly propagates probabilistic and possibilistic uncertainties is compared with a pure probabilistic uncertainty propagation. The comparison is carried out with reference to a risk model concerning the design of a flood protection dike

An informational distance for estimating the faithfulness of a possibility distribution, viewed as a family of probability distributions, with respect to data

International audienceAn acknowledged interpretation of possibility distributions in quantitative possibility theory is in terms of families of probabilities that are upper and lower bounded by the associated possibility and necessity measures. This paper proposes an informational distance function for possibility distributions that agrees with the above-mentioned view of possibility theory in the continuous and in the discrete cases. Especially, we show that, given a set of data following a probability distribution, the optimal possibility distribution with respect to our informational distance is the distribution obtained as the result of the probability-possibility transformation that agrees with the maximal specificity principle. It is also shown that when the optimal distribution is not available due to representation bias, maximizing this possibilistic informational distance provides more faithful results than approximating the probability distribution and then applying the probability-possibility transformation. We show that maximizing the possibilistic informational distance is equivalent to minimizing the squared distance to the unknown optimal possibility distribution. Two advantages of the proposed informational distance function is that (i) it does not require the knowledge of the shape of the probability distribution that underlies the data, and (ii) it amounts to sum up the elementary terms corresponding to the informational distance between the considered possibility distribution and each piece of data. We detail the particular case of triangular and trapezoidal possibility distributions and we show that any unimodal unknown probability distribution can be faithfully upper approximated by a triangular distribution obtained by optimizing the possibilistic informational distance

Possibilistic networks parameter learning: Preliminary empirical comparison

International audienceLike Bayesian networks, possibilistic ones compactly encode joint uncertainty representations over a set of variables. Learning possibilistic networks from data in general and from imperfect or scarce data in particular, has not received enough attention. Indeed, only few works deal with learning the structure and the parameters of a possibilistic network from a dataset. This paper provides a preliminary comparative empirical evaluation of two approaches for learning the parameters of a possibilistic network from empirical data. The first method is a possibilistic approach while the second one first learns imprecise probability measures then transforms them into possibility distributions by means of probability-possibility transformations. The comparative evaluation focuses on learning belief networks on datasets with missing data and scarce datasets

A possibilistic interpretation of ensemble forecasts: experiments on the imperfect Lorenz 96 system

Abstract. Ensemble forecasting has gained popularity in the field of numerical medium-range weather prediction as a means of handling the limitations inherent to predicting the behaviour of high dimensional, nonlinear systems, that have high sensitivity to initial conditions. Through small strategical perturbations of the initial conditions, and in some cases, stochastic parameterization schemes of the atmosphere-ocean dynamical equations, ensemble forecasting allows one to sample possible future scenarii in a Monte-Carlo like approximation. Results are generally interpreted in a probabilistic way by building a predictive density function from the ensemble of weather forecasts. However, such a probabilistic interpretation is regularly criticized for not being reliable, because of the chaotic nature of the dynamics of the atmospheric system as well as the fact that the ensembles of forecasts are not, in reality, produced in a probabilistic manner. To address these limitations, we propose a novel approach: a possibilistic interpretation of ensemble predictions, taking inspiration from fuzzy and possibility theories. Our approach is tested on an imperfect version of the Lorenz 96 model and results are compared against those given by a standard probabilistic ensemble dressing. The possibilistic framework reproduces (ROC curve, resolution) or improves (ignorance, sharpness, reliability) the performance metrics of a standard univariate probabilistic framework. This work provides a first step to answer the question whether probability distributions are the right tool to interpret ensembles predictions. </jats:p

Expression of uncertainty in fuzzy scales based measurements

International audienceFuzzy scales were introduced as a transition between weak scales and strong scales. Preceding studies on fuzzy scales considered only ideal exact measurement without any consideration of uncertainty. The goal of this paper is to present a general approach for the management of uncertainty within the context of fuzzy scale based measurements. After a short reminder on fuzzy scales, a method to define a probability density function or a possibility function on indications given by a fuzzy scale based measurement is exposed. Finally, a method based on the evidence theory is applied to build simultaneously a probability density function and an associated possibility function

A meta-cognitive architecture for planning in uncertain environments

Abstract The behavior of an artificial agent performing in a natural environment is influenced by many different pressures and needs coming from both external world and internal factors, which sometimes drive the agent to reach conflicting goals. At the same time, the interaction between an artificial agent and the environment is deeply affected by uncertainty due to the imprecision in the description of the world, and the unpredictability of the effects of the agent's actions. Such an agent needs meta-cognition in terms of both self-awareness and control. Self-awareness is related to the internal conditions that may possibly influence the completion of the task, while control is oriented to performing actions that maintain the internal model of the world and the perceptions aligned. In this work, a general meta-cognitive architecture is presented, which is aimed at overcoming these problems. The proposed architecture describes an artificial agent, which is capable to combine cognition and meta-cognition to solve problems in an uncertain world, while reconciling opposing requirements and goals. While executing a plan, such an agent reflects upon its actions and how they can be affected by its internal conditions, and starts a new goal setting process to cope with unforeseen changes. The work defines the concept of "believability" as a generic uncertain quantity, the operators to manage believability, and provides the reader with the u-MDP that is a novel MDP able to deal with uncertain quantities expressed as possibility, probability, and fuzziness. A couple u-MDPs are used to implement the agent's cognitive and meta-cognitive module. The last one is used to perceive both the physical resources of the agent's embodiment and the actions performed by the cognitive module in order to issue goal setting and re-planning actions