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International audience; Dealing with partially known or missing data is a common problem in machine learning. This work is interested in the problem of querying the true value of data to improve the quality of the learned model, when those data are only partially known. This study is in the line of active learning, since we consider that the precise value of some partial data can be queried to reduce the uncertainty in the learning process, yet can consider any kind of partial data (not only entirely missing one). We propose a querying strategy based on the concept of racing algorithms in which several models are competing. The idea is to identify the query that will help the most to quickly decide the winning model in the competition. After discussing and formalizing the general ideas of our approach, we study the particular case of decision trees in case of interval-valued features and setvalued labels. The experimental results indicate that, in comparison to other baselines, the proposed approach significantly outperforms simpler strategies in the case

International audience; Deep networks, like some other learning models, can associate high trust to unreliable predictions. Making these models robust and reliable is therefore essential, especially for critical decisions. This experimental paper shows that the conformal prediction approach brings a convincing solution to this challenge. Conformal prediction consists in predicting a set of classes covering the real class with a user-defined frequency. In the case of atypical examples, the conformal prediction will predict the empty set. Experiments show the good behavior of the conformal approach, especially when the data is noisy.

International audience; Measuring inconsistency has been and is still an active research topic in both logic and evidence theory. However, the two fields have developed distinct notions and measures of inconsistency, following different paths. In this paper, we attempt to build some first bridges between the two trends, suggesting some first means for one to enrich the other, and vice-versa.

There are relatively few works dealing with conformal prediction for multi-task learning issues, and this is particularly true for multi-target regression. This paper focuses on the problem of providing valid (i.e., frequency calibrated) multi-variate predictions. To do so, we propose to use copula functions applied to deep neural networks for inductive conformal prediction. We show that the proposed method ensures efficiency and validity for multi-target regression problems on various data sets., Comment: 17 pages, 8 figures, under review

International audience; We present two different strategies to extend the classical multi-label chaining approach to handle imprecise probability estimates. These estimates use convex sets of distributions (or credal sets) in order to describe our uncertainty rather than a precise one. The main reasons one could have for using such estimations are (1) to make cautious predictions (or no decision at all) when a high uncertainty is detected in the chaining and (2) to make better precise predictions by avoiding biases caused in early decisions in the chaining. We adapt both strategies to the case of the naive credal classifier, showing that this adaptations are computationally efficient. Our experimental results on missing labels, which investigate how reliable these predictions are in both approaches, indicate that our approaches produce relevant cautiousness on those hard-to-predict instances where the precise models fail.

International audience; Occupancy grids are common tools used in robotics to represent the robot environment, and that may be used to plan trajectories, select additional measurements to acquire, etc. However, deriving information about those occupancy grids from sensor measurements often induce a lot of uncertainty, especially for grid elements that correspond to occluded or far away area from the robot. This means that occupancy information may be quite uncertain and imprecise at some places, while being very accurate at others. Modelling finely this occupancy information is essential to decide the optimal action the robot should take, but a refined modelling of uncertainty often implies a higher computational cost, a prohibitive feature for real-time applications. In this paper, we introduce the notion of credal occupancy grids, using the very general theory of imprecise probabilities to model occupancy uncertainty. We also show how one can perform efficient, real-time inferences with such a model, and show a use-case applying the model to an autonomous vehicle trajectory planning problem.

Learning ranking models is a difficult task, in which data may be scarce and cautious predictions desirable. To address such issues, we explore the extension of the popular parametric probabilistic Plackett–Luce model, often used to model rankings, to the imprecise setting where estimated parameters are set-valued. In particular, we study how to achieve cautious or conservative inference with it, and illustrate their application on label ranking problems, a specific supervised learning task.

International audience; Neighbourhoods of precise probabilities are instrumental to perform robustness analysis, as they rely on very few parameters. In the rst part of this study, we introduced a general, unied view encompassing such neighbourhoods, and revisited some well-known models (pari mutuel, linear vacuous, constant odds-ratio). In this second part, we study models that have received little to no attention, but are induced by classical distances between probabilities, such as the total variation, the Kolmogorov and the L 1 distances. We nish by comparing those models in terms of a number of properties: precision , number of extreme points, n-monotonicity,. .. thus providing possible guidelines to select a neighbourhood rather than another.

International audience; Belief functions are quite generic models when it comes to represent uncertain data, as it extends a wide rangeof uncertainty models (possiblity and probability distributions, among others). Usually, belief functions are defined over finitespaces, however many real word problems require to deal with beliefs over a continuous space while maintaining computational efficiency. This paper discusses the case of focal sets on the unit simplex, and proposes efficient inference tools to manipulate them. Such sets can be used to represent unknown proportions that one may face in various fields like soil contamination managing, plastic sorting or image reconstruction. In this paper, we illustrate their use on an industrial problem of plastic sorting, where the proportion of material impurities must not go over a limit while minimizing the rejection of sorted materials, whose nature is uncertain.

International audience; Ranking problems are difficult to solve due to their combinatorial nature. One way to solve this issue is to adopt a decomposition scheme, splitting the initial difficult problem in many simpler problems. The predictions obtained from these simplified settings must then be combined into one single output, possibly resolving inconsistencies between the outputs. In this paper, we consider such an approach for the label ranking problem, where in addition we allow the predictive model to produce cautious inferences in the form of sets of rankings when it lacks information to produce reliable, precise predictions. More specifically , we propose to combine a rank-wise decomposition, in which every sub-problem becomes an ordinal classification one, with a constraint satisfaction problem (CSP) approach to verify the consistency of the predictions. Our experimental results indicate that our approach produces predictions with appropriately balanced reliability and precision, while remaining competitive with classical, precise approaches.

International audience; Predictions from classification models are most often used as final decisions. Yet, there are situations where the prediction serves as an input for another constrained decision problem. In this paper, we consider such an issue where the classifier provides imprecise and/or uncertain predictions that need to be managed within the decision problem. More precisely, we consider the optimisation of a mix of material pieces of different types in different containers. Information about those pieces is modelled by a mass function provided by a cautious classifier. Our proposal concerns the statement of the optimisation problem within the framework of belief function. Finally, we give an illustration of this problem in the case of plastic sorting for recycling purposes.

Modelling the preferences of a decision maker about alternatives having multiple criteria usually starts by collecting preference information (comparisons of alternatives, importance of criteria, …), which are then used to fit a preference model issued from some set of hypothesis (weighted average, CP-net, lexicographic orderings, AHP, …). In practice, this process often leads to inconsistencies that may be due to inaccurate information provided by the decision maker, who can be unsure about the provided information, or to a poor choice of hypothesis set, which can be too restrictive or not well adapted to the decision process. In this paper, we propose to use belief functions as a way to quantify and resolve such inconsistencies, notably by allowing the decision maker to express her/his certainty about the provided preferential information. Our framework is generic, in the sense that it does not assume a given set of hypothesis a priori, and is consistent with precise methods, in the sense that in the absence of uncertainty and inconsistencies in the information, precise models are ultimately retrieved.

International audience; Idempotence is a desirable property when cautiousness is wanted in an information fusion process, since in this case combining identical information should not lead to the reinforcement of some hypothesis. Idempotent operators also guarantee that identical information items are not counted twice in the fusion process, a very important property in decentralized applications where the information origin cannot always be tracked (ad-hoc wireless networks are typical examples). In the theory of belief functions, a sound way to combine conjunctively multiple information items is to design a combination rule that selects the least informative element among a subset of belief functions more informative than each of the combined ones. In contrast, disjunctive rules can be retrieved by selecting the most informative element among a subset of belief functions less informative than each of the combined ones. One interest of such approaches is that they provide idempotent rules by construction. The notions of less and more informative are often formalized through partial orderings extending usual set-inclusion, yet the only two informative partial orders that provide a straightforward idempotent rule leading to a unique result are those based on the conjunctive and disjunctive weight functions. In this article, we show that other partial orders can achieve a similar goal when the problem is slightly relaxed into a distance optimization one. Building upon previous work, this paper investigates the use of distances compatible with informative partial orders to determine a unique solution to the combination problem. The obtained operators are conjunctive/disjunctive, idempotent and commutative, but lack associativity. They are, however, quasi-associative allowing sequential combinations at no extra complexity. Some experiments demonstrate interesting discrepancies as compared to existing approaches, notably with the aforementioned rules relying on weight functions.

International audience; Indeterminate classifiers are cautious models able to predict more than one class in case of high uncertainty. A problem that arises when using such classifiers is how to evaluate their performances. This problem has already been considered in the case where all prediction errors have equivalent costs (that we will refer as the ''0/1 costs'' or accuracy setting). The purpose of this paper is to study the case of generic cost functions. We provide some properties that the costs of indeterminate predictions could or should follow, and review existing proposals in the light of those properties. This allows us to propose a general formula fitting our properties that can be used to produce and evaluate indeterminate predictions. Some experiments on the cost-sensitive problem of ordinal regression illustrate the behavior of the proposed evaluation criterion.

International audience; Within imprecise probability theory, the extreme points of convex probability sets have an important practical role (to perform inference on graphical models, to compute expectation bounds,. . .). This is especially true for sets presenting specic features that make them easy to manipulate in applications. This easiness is the reason why extreme points of such models (probability intervals, possibility distributions,. . .) have been well studied. Yet, imprecise cumulative distributions (a.k.a. p-boxes) constitute an important exception, as the characterization of their extreme points remain to be studied. This is what we do in this paper, where we characterize the maximal number of extreme points of a p-box, give a family of p-boxes that attains this number and show an algorithm that allows to compute the extreme points of a given p-box. To achieve all this, we also provide what we think to be a new characterization of extreme points of a belief function.

International audience; Neighbourhoods of precise probabilities are instrumental to perform robustness analysis, as they rely on very few parameters. Many such models, sometimes referred to as distortion models, have been proposed in the literature, such as the pari mutuel model, the linear vacuous mixtures or the constant odds ratio model. This paper is the rst part of a two paper series where we study the sets of probabilities induced by such models, regarding them as neighbourhoods dened over specic metrics or premetrics. We also compare them in terms of a number of properties: precision, number of extreme points, n-monotonicity, behaviour under conditioning, etc. This rst part tackles this study on some of the most popular distortion models in the literature, while the second part studies less known neighbourhood models and summarises our findings.

Convolution kernels are essential tools in signal processing: they are used to filter noisy signal, interpolate discrete signals, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ldots $$\end{document}. However, in a given application, it is often hard to select an optimal shape of the kernel. This is why, in practice, it may be useful to possess efficient tools to perform a robustness analysis, talking the form in our case of an imprecise convolution. When convolution kernels are positive, their formal equivalence with probability distributions allows one to use imprecise probability theory to achieve such an imprecise convolution. However, many kernels can have negative values, in which case the previous equivalence does not hold anymore. Yet, we show mathematically in this paper that, while the formal equivalence is lost, the computational tools used to describe sets of probabilities by intervals on the singletons still retain their key properties when used to approximate sets of (possibly) non-positive kernels. We then illustrate their use on a single application that consists of filtering a human electrocardiogram signal by using a low-pass filter whose order is imprecisely known. We show, in this experiment, that the proposed approach leads to tighter bounds than previously proposed approaches.

When classifying an example on the basis of an observed population of (training) samples, at least three kinds of situations can arise where picking a single class may be difficult: high aleatory uncertainty due to the natural mixing of classes, high epistemic uncertainty due to the scarcity of training data, and non-conformity or atypicality of the example with respect to observations made so far. While the two first kinds of situations have been explored extensively, the last one still calls for a principled analysis. This paper is a first proposal to address this issue within the theory of belief function.

The problem of learning from imprecise data has recently attracted increasing attention, and various methods to tackle this problem have been proposed. In this paper, we discuss and compare two quite opposite approaches, an “optimistic” one that interprets imprecise data in a way that is most favourable for a candidate model, and a “pessimistic” one in which model choice is guided by the most unfavourable interpretation. To avoid an overly extreme behaviour, a modified version of the latter has recently been proposed, which we complement by an adjusted version of the optimistic approach. By presenting the various methods within a common (loss minimization) framework and discussing illustrative examples, we hope to provide some insight into important properties and differences, thereby paving the way for a more formal analysis.

Various strategies for active learning have been proposed in the machine learning literature. In uncertainty sampling, which is among the most popular approaches, the active learner sequentially queries the label of those instances for which its current prediction is maximally uncertain. The predictions as well as the measures used to quantify the degree of uncertainty, such as entropy, are almost exclusively of a probabilistic nature. In this paper, we advocate a distinction between two different types of uncertainty, referred to as epistemic and aleatoric, in the context of active learning. Roughly speaking, these notions capture the reducible and the irreducible part of the total uncertainty in a prediction, respectively. We conjecture that, in uncertainty sampling, the usefulness of an instance is better reflected by its epistemic than by its aleatoric uncertainty. This leads us to suggest the principle of "epistemic uncertainty sampling", which we instantiate by means of a concrete approach for measuring epistemic and aleatoric uncertainty. In experimental studies, epistemic uncertainty sampling does indeed show promising performance., Draft version of a paper to be published in the proceedings of DS 2019, 22nd International Conference on Discovery Science, Split, Croatia, 2019

International audience; In uncertainty theories, a common problem is to define how we can extend relations between sets (e.g., inclusion, ranking, consistency, …) to corresponding notions between uncertainty representations. Such definitions can then be used to perform the same operations as those that are done for sets: comparing information content, ordering alternatives or checking consistency, to name a few. In this paper, we propose a general way to extend set relations to belief functions, using constrained stochastic matrices to identify those belief functions in relation. We then study some properties of our proposal, as well as its connections with existing works focusing on specific relations.

International audience; Gaussian discriminant analysis is a popular classification model, that in the precise case can produce unreliable predictions in case of high uncertainty. While imprecise probability theory offer a nice theoretical framework to solve this issue, it has not been yet applied to Gaussian discriminant analysis. This work remedies this, by proposing a new Gaussian discrimi-nant analysis based on robust Bayesian analysis and near-ignorance priors. The model delivers cautious predictions, in form of set-valued class, in case of limited or imperfect available information. Experiments show that including an imprecise component in the Gaussian discriminant analysis produces reasonably cautious predictions, in the sense that the number of set-valued predictions is not too high, and that those predictions correspond to hard-to-classify instances, that is instances for which the precise classifier accuracy drops.

International audience; Preference elicitation is a key element of any multi-criteria decision analysis (MCDA) problem, and more generally of individual user preference learning. Existing efficient elicitation procedures in the literature mostly use either robust or Bayesian approaches. In this paper, we are interested in extending the former ones by allowing the user to express uncertainty in addition of her preferential information and by modelling it through belief functions. We show that doing this, we preserve the strong guarantees of robust approaches, while overcoming some of their drawbacks. In particular, our approach allows the user to contradict herself, therefore allowing us to detect inconsistencies or ill-chosen model, something that is impossible with more classical robust methods.

International audience; The pari-mutuel model is a betting scheme that has its origins in horse racing, and that has been applied in a number of contexts, mostly economics. In this paper, we consider the set of probability measures compatible with a pari-mutuel model, characterize its extreme points, and investigate the properties of the associated lower and upper probabilities. We show that the pari-mutuel model can be embedded within the theory of probability intervals, and prove necessary and sucient conditions for it to be a belief function or a minitive measure. In addition, we also investigate the combination of dierent pari-mutuel models and their denition on product spaces.

International audience; In this paper, we study how cautious conclusions should be taken when considering interval-valued propositional logic, that is logic where to each formula is associated a real-valued interval providing imprecise information about the penalty incurred for falsifying this formula. We work under the general assumption that the weights of falsified formulas are aggregated through a non-decreasing commutative function, and that an interpretation is all the more plausible as it is less penalized. We then formulate some dominance notions, as well as properties that such notions should follow if we want to draw conclusions that are at the same time informative and cautious. We then discuss the dominance notions in light of such properties.

International audience; In this paper, we explore the problem of estimating lower and upper densities from imprecisely defined families of parametric kernels. Such estimations allow to rely on a single bandwidth value, and we show that it provides good results on classification tasks when extending the naive Bayesian classifier

In uncertainty theories, a common problem is to define how we can extend relations between sets (e.g., inclusion, ranking, consistency, ...) to corresponding notions between uncertainty representations. Such definitions can then be used to perform the same operations as those that are done for sets: measuring information content, ordering alternatives or checking consistency, to name a few. In this paper, we propose a general way to extend set relations to belief functions, using constrained stochastic matrices to identify those belief functions in relation. We then study some properties of our proposal, as well as its relations with existing works focusing on peculiar relations.

We propose a method for reliable prediction in multi-class classification, where reliability refers to the possibility of partial abstention in cases of uncertainty. More specifically, we allow for predictions in the form of preorder relations on the set of classes, thereby generalizing the idea of set-valued predictions. Our approach relies on combining learning by pairwise comparison with a recent proposal for modeling uncertainty in classification, in which a distinction is made between reducible (a.k.a. epistemic) uncertainty caused by a lack of information and irreducible (a.k.a. aleatoric) uncertainty due to intrinsic randomness. The problem of combining uncertain pairwise predictions into a most plausible preorder is then formalized as an integer programming problem. Experimentally, we show that our method is able to appropriately balance reliability and precision of predictions.

International audience; In this paper, we are interested in the label ranking problem. We are more specifically interested in the recent trend consisting in predicting partial but more accurate (i. e. , making less incorrect statements) orders rather than complete ones. To do so, we propose a ranking method based on label-wise decomposition. We estimate an imprecise probabilistic model over each label rank and we infer a partial order from it using optimisation techniques. This leads to new results concerning a particular bilinear assignment problem. Finally, we provide some experiments showing the feasibility of our method.

In this paper, we study the conjunction of possibility measures when they are interpreted as coherent upper probabilities, that is, as upper bounds for some set of probability measures. We identify conditions under which the minimum of two possibility measures remains a possibility measure. We provide graphical way to check these conditions, by means of a zero-sum game formulation of the problem. This also gives us a nice way to adjust the initial possibility measures so their minimum is guaranteed to be a possibility measure. Finally, we identify conditions under which the minimum of two possibility measures is a coherent upper probability, or in other words, conditions under which the minimum of two possibility measures is an exact upper bound for the intersection of the credal sets of those two possibility measures., Comment: 23 pages, 2 figures

International audience; Two variables are called comonotone when there is an increasing relation between them, in the sense that when one of them increases (decreases), so does the other one. This notion has been widely investigated in probability theory, and is related to copulas. This contribution studies how the notion of comonotonicity can be extended to an imprecise setting on discrete spaces, where probabilities are only known to belong to a convex set. We define comonotonicity for such sets and investigate its characterizations in terms of lower probabilities, as well as its connection with copulas. As this theoretical characterization can be tricky to apply to general lower probabilities, we also investigate specific models of practical importance. In particular, we provide some sufficient conditions for a comonotone belief function with fixed marginals to exist, and characterize comonotone bivariate p-boxes.

We propose in this article a new relational clustering method that can return a partial answer (i.e., a set of clusterings) in some cases. Starting from relational or similarity data, we determine a partial equivalence relation defined on the set of objects (two objects are linked if they belong to the same cluster): the key idea is to allow the method to abstain on some pairwise links because they cannot be determined with enough certainty from the data. This cautious equivalence relation represents a set of possible hard clusterings which can be obtained by completing the partial relation. This formalization makes it possible to easily detect ambiguous links and to identify subsets of objects with uncertain relationship. We illustrate the potential interest of our approach as a tool for exploratory data analysis of synthetic and real data sets.

International audience; In this paper, we introduce a generic way to represent and manipulate pairwise information about partial orders (representing rankings, preferences, ...) with belief functions. We provide generic and practical tools to make inferences from this pairwise information and illustrate their use onthe machine learning problems that are label ranking and multi-label prediction. Our approach differs from most other quantitative approaches handling complete or partial orders, in the sense that partial orders are here considered as primary objects and not as incomplete specifications of ideal but unknown complete orders.

This paper studies the problem of providing predictions with a K-nn approach when data have partial features given in the form of intervals. To do so, we adopt an optimistic approach to replace the ill-known values, that requires to compute sets of possible and necessary neighbours of an instance. We provide an easy way to compute such sets, as well as the decision rule that follows from them. Our approach is then compared to a simple imputation method in different scenarios, in order to identify those ones where it is advantageous.

International audience; In some applications of machine learning and information retrieval (e.g. medical diagnosis, image recognition, pre-classification...), it can be preferable to provide less informative but more reliable predictions. This can be done by making partial predictions in the form of class subsets when the available information is insufficient to provide a reliable unique class. Imprecise probabilistic approaches offer nice tools to learn models from which such cautious predictions can be produced. However, the learning and inference processes of such models are computationally harder than their precise counterparts. In this paper, we introduce and study a particular binary decomposition strategy, nested dichotomies, that offer computational advantages in both the learning (due to the binarization process) and the inference (due to the decomposition strategy) processes. We show with experiments that these computational advantages do not lower the performances of the classifiers, and can even improve them when the class space has some structure.

Modelling the preferences of a decision maker about multi-criteria alternatives usually starts by collecting preference information, then used to fit a model issued from a set of hypothesis (weighted average, CP-net). This can lead to inconsistencies, due to inaccurate information provided by the decision maker or to a poor choice of hypothesis set. We propose to quantify and resolve such inconsistencies, by allowing the decision maker to express her/his certainty about the provided preferential information in the form of belief functions.

When having to make a prediction under probabilistic uncertainty in ordinal problems, the median offers a number of interesting properties compared to other statistics such as the expected value. In particular, it does not depend on a particular metric defined over the elements, but still takes account of the ordinal nature of the data. It can also be shown to be the minimizer of the $$L_1$$ loss function. In this paper, we show that similar results can be obtained when the uncertainty is described not by a single probability distribution, but by a convex set of those. In particular, we relate the lower and upper medians to the $$L_1$$ loss function via the notion of lower and upper expectations (and extend these results to general quantiles). We also show that, using a different decision rule, the lower and upper median can be retrieved when assuming the cost to be strictly monotonic and symmetric, and nothing more. Finally, we run some tests to show the interest of using Median based predictions with convex sets of probabilities in ordinal regression problems.

International audience; In this paper, we address the problem of optimally querying a single expert to reduce set (interval) uncertainty. We propose optimal querying strategies for two particular query formats (local bound and pair wise comparisons) based on two main selection criteria (the minimax and the Bayesian rules). We study the computational aspects of the optimal solution in the general case and for the specific functions of practical interest (monotonic and multi-linear). The use of the proposed approach is illustrated through numerical simulations on a common estimation problem in reliability analysis.

Knowledge regarding complex systems are heterogeneous and fragmented.modelling dynamic complex systems in the framework of dynamic credal networks.practical methodology coupling Dirichlet distributions with interval probabilities to incrementally build and update model parameters whatever source and format of knowledge.enables to take into account (1) stochastic and epistemic uncertainties pertaining to the system; (2) the confidence level on the different sources of information.illustrate the application of the methodology to the modelling of a simplified industrial case study. Modeling complex dynamical systems from heterogeneous pieces of knowledge varying in precision and reliability is a challenging task. We propose the combination of dynamical Bayesian networks and of imprecise probabilities to solve it. In order to limit the computational burden and to make interpretation easier, we also propose to encode pieces of (numerical) knowledge as probability intervals, which are then used in an imprecise Dirichlet model to update our knowledge. The idea is to obtain a model flexible enough so that it can easily cope with different uncertainties (i.e., stochastic and epistemic), integrate new pieces of knowledge as they arrive and be of limited computational complexity.

International audience; So-called credal classifiers offer an interesting approach when the reliability or robustness of predictions have to be guaranteed. Through the use of convex probability sets, they can select multiple classes as prediction when information is insufficient and predict a unique class only when the available information is rich enough. The goal of this paper is to explore whether this particular feature can be used advantageously in the setting of co-training, in which a classifier strengthen another one by feeding it with new labeled data. We propose several co-training strategies to exploit the potential indeterminacy of credal classifiers and test them on several UCI datasets. We then compare the best strategy to the standard co-training process to check its efficiency.

International audience; Hidden Markov models are popular tools for gesture recognition. Once the generative processes of gestures have been identified, an observation sequence is usually classified as the gesture having the highest likelihood, thus ignoring possible prior information. In this paper, we consider two potential improvements of such methods: the inclusion of prior information, and the possibility of considering convex sets of probabilities (in the likelihoods and the prior) to infer imprecise, but more reliable, predictions when information is insufficient. We apply the proposed approach to technical gestures, typically characterized by severe class imbalance. By modelling such imbalances as a prior information, we achieve more accurate results, while the imprecise quantification is shown to produce more reliable estimates.

We define a decision support system for eco-efficient biorefinery process comparison.Uncertainty is managed all along the pipeline for eco-design indicator computations.Data extraction from textual documents is guided by a Termino-ontological resource.Flexible structured database querying is guided by a Termino-ontological resource. Enzymatic hydrolysis of the main components of lignocellulosic biomass is one of the promising methods to further upgrading it into biofuels. Biomass pre-treatment is an essential step in order to reduce cellulose crystallinity, increase surface and porosity and separate the major constituents of biomass. Scientific literature in this domain is increasing fast and could be a valuable source of data. As these abundant scientific data are mostly in textual format and heterogeneously structured, using them to compute biomass pre-treatment efficiency is not straightforward. This paper presents the implementation of a Decision Support System (DSS) based on an original pipeline coupling knowledge engineering (KE) based on semantic web technologies, soft computing techniques and environmental factor computation. The DSS allows using data found in the literature to assess environmental sustainability of biorefinery systems. The pipeline permits to: (1) structure and integrate relevant experimental data, (2) assess data source reliability, (3) compute and visualize green indicators taking into account data imprecision and source reliability. This pipeline has been made possible thanks to innovative researches in the coupling of ontologies, uncertainty management and propagation. In this first version, data acquisition is done by experts and facilitated by a termino-ontological resource. Data source reliability assessment is based on domain knowledge and done by experts. The operational prototype has been used by field experts on a realistic use case (rice straw). The obtained results have validated the usefulness of the system. Further work will address the question of a higher automation level for data acquisition and data source reliability assessment.

International audience; In reliability analysis, comparing system reliability is an essential task when designing safe systems. When the failure probabilities of the system components (assumed to be independent) are precisely known, this task is relatively simple to achieve, as system reliabilities are precise numbers. When failure probabilities are ill-known (known to lie in an interval) and we want to have guaranteed comparisons (i.e., declare a system more reliable than another when it is for any possible probability value), there are different ways to compare system reliabilities. We explore the computational problems posed by such extensions, providing first insights about their pros and cons.

Distances between mass functions are instrumental tools in evidence theory, yet it is not always clear in which situation a particular distance should be used. Indeed, while the mathematical properties of distances have been well studied, how to interpret them is still a largely open issue. As a step towards answering this question, we propose to interpret distances by looking at their compatibility with partial orders. We formalize this compatibility through some mathematical properties thereby allowing to combine the advantages of both partial orders (clear semantics) and distances (richer structure and access to numerical tools). We explore in particular the case of informational partial orders, and how distances compatible with such orders can be used to approximate initial belief functions by simpler ones through the use of convex optimization. We finish by discussing some perspectives of the current work. Distances and partial orders in the theory of belief functions are formally related through a desirable property.The compatibility of several L k norm based distances with some informational partial orders is proved.These results are exploited to approximate initial belief functions by simpler ones through the use of convex optimization.

A pair of lower and upper cumulative distribution functions, also called probability box or p-box, is among the most popular models used in imprecise probability theory. They arise naturally in expert elicitation, for instance in cases where bounds are specified on the quantiles of a random variable, or when quantiles are specified only at a finite number of points. Many practical and formal results concerning p-boxes already exist in the literature. In this paper, we provide new efficient tools to construct multivariate p-boxes and develop algorithms to draw inferences from them. For this purpose, we formalise and extend the theory of p-boxes using Walley's behavioural theory of imprecise probabilities, and heavily rely on its notion of natural extension and existing results about independence modeling. In particular, we allow p-boxes to be defined on arbitrary totally preordered spaces, hence thereby also admitting multivariate p-boxes via probability bounds over any collection of nested sets. We focus on the cases of independence (using the factorization property), and of unknown dependence (using the Fr\'echet bounds), and we show that our approach extends the probabilistic arithmetic of Williamson and Downs. Two design problems---a damped oscillator, and a river dike---demonstrate the practical feasibility of our results., Comment: 33 pages, 8 figures; v2: added keywords, added doi link

Contact: destercke@supagro.inra.fr, sdestercke@gmail.com; International audience; Information is said to be bipolar when it has a positive and a negative part. The problem of representing and processing such bipolar information has recently received a lot of attention in uncertainty theories. In this paper, we are concerned with the representation of asymmetric bipolarity, i.e., with situations where positive and negative information are unrelated and processed in parallel. In this latter case, positive information consists of observations of experiment results, showing what values are possible, whereas negative information consists of constraints (e.g., provided by an expert), restricting the range of possible variable values. Up to now, there are no proposition as to how such bipolar information can be treated in the framework of imprecise probability theory, i.e., when information is represented by convex sets of probabilities. In this paper, we propose the basis of such a framework and provide some illustrative examples.

International audience; This paper is a fine review of various aspects related to the statistical handling of "on-tic" random fuzzy sets by the means of appropriate distances. It is quite comprehensive and helpful, as it clarifies the status of fuzzy sets in such methods, explains the advan-tages of using a distance-based approach, specifies the pitfalls in which one should not fall when dealing with "ontic" random fuzzy sets and provides some illustration of practical computations. Not being a statistician but an occasional user of statistics, my discussion will mainly focus on this more practical aspect.

Axe 5 Application intégrée de la connaissance, de l’information et des technologies permettant d’accroître la qualité et la sécurité des aliments Contact : sdestercke@gmail.com; International audience; 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.