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Description:
We consider a particular fuzzy-stochastic PDE depending on the interaction of probabilistic and non-probabilistic (via fuzzy arithmetic in terms of possibility theory) influences. Such a combination is beneficial in an engineering context, where aleatoric and epistemic uncertainties appear simultaneously. The fuzzy-stochastic dependence is described in a high-dimensional parameter space, thus easily leading to an exponential complexity in practical computations. To alleviate this severe obstacle, a compressed low-rank approximation in form of Hierarchical Tucker representation of the desired parametric quantity of interest is derived. The performance of the proposed model order reduction approach is demonstrated.