Eric Chojnacki

Unifying practical uncertainty representations -- I: Generalized p-boxes

There exist several simple representations of uncertainty that are easier to handle than more general ones. Among them are random sets, possibility distributions, probability intervals, and more recently Fersons p-boxes and Neumaiers clouds. Both for theoretical and practical considerations, it is very useful to know whether one representation is equivalent to or can be approximated by other ones. In this paper, we define a generalized form of usual p-boxes. These generalized p-boxes have interesting connections with other previously known representations. In particular, we show that they are equivalent to pairs of possibility distributions, and that they are special kinds of random sets. They are also the missing link between p-boxes and clouds, which are the topic of the second part of this study.

Unifying practical uncertainty representations. II: Clouds

There exist many simple tools for jointly capturing variability and incomplete information by means of uncertainty representations. Among them are random sets, possibility distributions, probability intervals, and the more recent Fersons p-boxes and Neumaiers clouds, both defined by pairs of possibility distributions. In the companion paper, we have extensively studied a generalized form of p-box and situated it with respect to other models. This paper focuses on the links between clouds and other representations. Generalized p-boxes are shown to be clouds with comonotonic distributions. In general, clouds cannot always be represented by random sets, in fact not even by two-monotone (convex) capacities.

Cautious Conjunctive Merging of Belief Functions

When merging belief functions, Dempster rule of combination is justified only when information sources can be considered as independent. When this is not the case, one must find out a cautious merging rule that adds a minimal amount of information to the inputs. Such a rule is said to follow the principle of minimal commitment. Some conditions it should comply with are studied. A cautious merging rule based on maximizing expected cardinality of the resulting belief function is proposed. It recovers the minimum operation when specialized to possibility distributions. This form of the minimal commitment principle is discussed, in particular its discriminating power and its justification when some conflict is present between the belief functions.

How to manage natural risks in mountain areas in a context of imperfect information? New frameworks and paradigms for expert assessments and decision-making

In mountain areas, natural phenomena such as snow avalanches, debris flows and rock-falls, put people and objects at risk with sometimes dramatic consequences. Risk is classically considered as a combination of hazard, the combination of the intensity and frequency of the phenomenon, and vulnerability which corresponds to the consequences of the phenomenon on exposed people and material assets. Risk management consists in identifying the risk level as well as choosing the best strategies for risk prevention, i.e. mitigation. In the context of natural phenomena in mountainous areas, technical and scientific knowledge is often lacking. Risk management decisions are therefore based on imperfect information. This information comes from more or less reliable sources ranging from historical data, expert assessments, numerical simulations etc. Finally, risk management decisions are the result of complex knowledge management and reasoning processes. Tracing the information and propagating information quality from data acquisition to decisions are therefore important steps in the decision-making process. In this paper, a global integrated framework is proposed to improve the risk management process in a context of information imperfection provided by more or less reliable sources. It includes uncertainty as well as imprecision, inconsistency and incompleteness. It is original in the methods used and their association: sequential decision context description, development of specific decision-making methods, imperfection propagation in numerical modelling and information fusion. This framework not only assists in decision-making but also traces the process and evaluates the impact of information quality on decision-making.

Possibilistic information fusion using maximal coherent subsets

When multiple sources provide information about the same unknown quantity, their fusion into a synthetic interpretable message is often a tedious problem, especially when sources are conflicting. In this paper, we propose to use possibility theory and the notion of maximal coherent subsets, often used in logic-based representations, to build a fuzzy belief structure that will be instrumental both for extracting useful information about various features of the information conveyed by the sources and for compressing this information into a unique possibility distribution.

Numerical accuracy and efficiency in the propagation of epistemic and aleatory uncertainties

The need to differentiate between epistemic and aleatory uncertainties is now well admitted by the risk analysis community. One way to do so is to model aleatory uncertainty by classical probability distributions and epistemic uncertainty by means of possibility distributions, and then propagate them by their respective calculus. The result of this propagation is a random fuzzy variable. When dealing with complex models, the computational cost of such a propagation quickly becomes too high. In this paper, we propose a numerical approach, the Random/Fuzzy (RaFu) method, whose aim is to determine an optimal numerical strategy so that computational costs are reduced to their minimum, using the theoretical frameworks mentioned above. We also give some means to take account of the resulting numerical error. The benefits of the RaFu method are shown by comparing it to previously proposed methods.

A CONSONANT APPROXIMATION OF THE PRODUCT OF INDEPENDENT CONSONANT RANDOM SETS

The belief structure resulting from the combination of consonant and independent marginal random sets is not, in general, consonant. Also, the complexity of such a structure grows exponentially with the number of combined random sets, making it quickly intractable for computations. In this paper, we propose a simple guaranteed consonant outer approximation of this structure. The complexity of this outer approximation does not increase with the number of marginal random sets (i.e., of dimensions), making it easier to handle in uncertainty propagation. Features and advantages of this outer approximation are then discussed, with the help of some illustrative examples.

Optimisation of internal contamination monitoring programme by integration of uncertainties.

Potential internal contamination of workers is monitored by periodic bioassay measurements interpreted in terms of intake and committed effective dose by the use of biokinetic and dosimetric models. After a prospective evaluation of exposure at a workplace, a suitable monitoring programme can be defined by choosing adequate measurement techniques and frequency. In this study, the sensitivity of a programme is evaluated by the minimum intake and dose, which may be detected with a given level of confidence by taking into account uncertainties on exposure conditions and measurements. This is made for programme optimisation, which is performed by comparing the sensitivities of different alternative programmes. These methods were applied at the AREVA NC reprocessing plant and support the current monitoring programme as the best compromise between the cost of the measurements and the sensitivity of the programme.

Coupling GIS and Multi-Criteria Modeling to Support Post-Accident Nuclear Risk Evaluation

In case of an accident concerning a nuclear installation, two intervention phases are distinguished: an emergency phase which calls for a rapid and organized response through intervention plans, and a post-accidental phase in which postponed actions are carried out on medium and/or long-term so that the situation comes back to a state judged as acceptable by stakeholders. The PRIME project has developed a decision aiding tool for risk managers involved in an industrial accident involving radioactive substances, through the evaluation of radio-ecological sensitivity of a territory in a post-accidental phase. The proposed decision aiding tool is grounded on the integration of Multiple Criteria Decision Aid (MCDA) and a Geographical Information System (GIS). The proposed methodology relies on the concept of decision map which corresponds to a planar subdivision of the territory in which each subdivision is evaluated on the basis of several criterion maps. This results in a set of disjoint spatial units evaluated on an ordinal scale using the ELECTRE TRI method. Hence, the result is a decision map representing the radio-ecological sensitivity of the territory; such maps prove to be very useful for stakeholders to design relevant post-accidental strategies.

Collective dosimetry to distinguish occupational exposure to natural uranium from alimentary uranium background in bioassay measurements

Abstract Purpose: To assess occupational exposure from uranium bioassay results which are low and impacted by dietary intakes. Material and methods: First, the bioassay results of a group of workers exposed to UO2 were compiled along with results of a control group. A Bayesian approach was developed to account for dietary intakes in the calculation of the committed effective dose from occupational exposure of a group of workers. Results: Significant differences in uranium bioassay between the exposed and control groups were found establishing an occupational contamination of the exposed group of workers. Because uranium alimentary excretion estimated from the control group is very variable leading to unreliable individual dose assessment, a collective dosimetric approach was chosen. Applying the Bayesian method, all annual committed effective doses for the exposed group were estimated to be below 0.5 mSv with 95% confidence. Conclusions: The Bayesian method presented here is well designed to derive best estimate and dose distribution for a group of workers when a contamination is difficult to discriminate from a natural background or alimentary excretion.