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Recent Trends in the Modeling and Quantification of Non-probabilistic Uncertainty

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Abstract

This paper gives an overview of recent advances in the field of non-probabilistic uncertainty quantification. Both techniques for the forward propagation and inverse quantification of interval and fuzzy uncertainty are discussed. Also the modeling of spatial uncertainty in an interval and fuzzy context is discussed. An in depth discussion of a recently introduced method for the inverse quantification of spatial interval uncertainty is provided and its performance is illustrated using a case studies taken from literature. It is shown that the method enables an accurate quantification of spatial uncertainty under very low data availability and with a very limited amount of assumptions on the underlying uncertainty. Finally, also a conceptual comparison with the class of Bayesian methods for uncertainty quantification is provided.

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Acknowledgements

The authors would like to acknowledge the financial support of the Flemish Research Foundation in the context of the research grant HIDIF (High dimensional interval fields) under grant number G0C2218N, as for the post-doctoral research grant 12P3519N of Matthias Faes.

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Faes, M., Moens, D. Recent Trends in the Modeling and Quantification of Non-probabilistic Uncertainty. Arch Computat Methods Eng 27, 633–671 (2020). https://doi.org/10.1007/s11831-019-09327-x

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