International audience; Distinguishing between two facets of uncertainty has become a standard practice in risk analysis, namely aleatory (representing variability) and epistemic (due to lack of knowledge). For representing aleatory uncertainty, there is a large consensus in the community about the use of probabilities under the frequentist perspective. However, for representing epistemic uncertainty, no unique straightforward answer exists. The different belief systems about the appropriate setting for uncertainty representation induce ontological-type uncertainty. Depending on how this representation is conducted might impact the decision-making phase especially when the chosen approach fails to provide a clear and transparent picture of the background knowledge underlying the risk analysis (Aven 2016).For representing epistemic uncertainty, several authors have advocated the use of subjective probabilities interpreted as beliefs (perceptions) about the probabilistic model within the Bayesian setting. Yet, when the “background knowledge is weak”, i.e. in situations where the available data are imprecise, diffuse, fluctuating, incomplete, fragmentary, vague, ambiguous, etc. (e.g., Dubois 2010), expressing uncertainties in the form of subjective probabilities may often be too “rich”: the identification of the probability distribution requires more information than what an expert may be able to supply, which is often restricted to the 0.50 and 0.95 fractiles or a prescribed mode and a support (Dubois and Prade 1994). Alternative uncertainty theories termed as “extra-probabilistic” (possibility theory, belief theory, imprecise probability, etc.) have been developped over the past years, which go beyond the systematic use of a single probabilistic law. The pillar of these theories is that many of such probabilistic laws may exist given the pieces of available information: these advocate bounding instead of providing a single uncertainty (probabilistic) model.In the present contribution, we analyse the pros and cons of this bounding strategy with a special focus on possibility theory. The analysis is peformed by comparison with conservative approaches using safety margins and traditional pure probabilistic approach by means of applications in the field of CO2 geological storage (Loschetter et al. 2015) and in natural hazard assessments (Rohmer and Baudrit 2011). We show that: 1. the possibility theory is a flexible setting for handling a broad range of different situations of epistemic uncertainty (e.g., representing and reasoning with vague concepts; handling imprecision; dealing with a probabilistic model whose parameters are ill-known); 2. the bounding strategy enables to convey an intuitive, understandable, transparent and communication-facilitating message on the level of epismetic uncertainty, i.e. on what is unknown.The other side of the coin is the level of sophistication added by the bounding strategy. Picturing the “flaws in the assessment process” using bounds may help the decision-making process by clearly displaying the limitations of the predictions instead of giving outcomes with an artificially high level of confidence. However, if the message on bounds is not transferred cautiously from scientists to end-users, this might undermine the confidence in the risk analysis, potentially leading to a loss of credibility in the results. A possible line of improvement is discussed through sensitivity and robustness characterisation.ReferencesAven, T. (2016). Risk assessment and risk management: Review of recent advances on their foundation. European Journal of Operational Research, 253(1), 1-13.Dubois, D. (2010). Representation, propagation, and decision issues in risk analysis under incomplete probabilistic information. Risk analysis, 30(3), 361-368.Dubois, D., Prade, H. (1994). Possibility theory and data fusion in poorly informed environments. Control Eng. Pract. 2, 811–823.Loschetter, A., Rohmer, J., de Lary, L., and Manceau, J. (2015). Dealing with uncertainty in risk assessments in early stages of a CO2 geological storage project: comparison of pure-probabilistic and fuzzy-probabilistic frameworks. Stochastic Environmental Research and Risk Assessment, 1–17.Rohmer, J. and Baudrit, C. (2011). The use of the possibility theory to investigate the epistemic uncertainties within scenario-based earthquake risk assessments. Natural hazards, 56(3), 613–632.