A framework for risk assessment during natural hazard based on the Choquet integral and MACBETH

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Abstract. Risk assessment in the face of natural disasters is an increasingly critical issue with climate change. Evaluating risk involves two distinct assessments: first, the probability of the disaster occurring, and second, the potential stakes or impacts of such an event. These impacts are generally categorized along several dimensions, notably human factors and infrastructure concerns. However, even when focusing solely on human stakes, characterizing risk –particularly in terms of the potential to prevent casualties– is complex. The most common approach to this problem relies on a weighted sum, which assigns specific weights to each criterion. This method effectively establishes the relative importance of one criterion over another and has the advantage of being linear. However, it also presents certain limitations. In particular, its linearity prevents it from capturing interactions between criteria, such as veto effects. In this paper, we propose a risk mapping method that utilizes an alternative aggregation function. Specifically, we rely on the Choquet integral, which allows for the modeling of interactions between criteria, whether in terms of complementarity or substitutability, while maintaining desirable properties such as monotonicity.We evaluate our approach by applying it to the challenge addressed in the MOGEC project: coastal flooding projections under IPCC’s RCP 8.5 scenario in the Pays-de-la-Loire region, following a storm of similar magnitude to Xynthia. For this assessment, we rely on the expertise of emergency response teams, for whom risk mapping is a key concern. Specifically, we demonstrate the advantages and limitations of our approach in the municipality of Batz-sur-Mer within this projected scenario.

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