(untitled) (REC 2026 - 11th International Workshop on Reliable Engineering Computing: Reliability Computations in a Data and Model-Driven World, 2026)
In order to realistically characterize data uncertainty in engineering – and consequently to reliably assess safety – it is required to thoroughly investigate spatial and temporal dependencies of uncertainty, e.g. in material characteristics, geometrical or environmental parameters. Recognizing the fact that probability-based approaches are inappropriate for databases with a severe lack of knowledge, purely epistemic uncertainty concepts for modeling dependent quantities are required. Several approaches to convex dependency modeling of interval quantities, as well as proposals for spatially dependent interval/fuzzy uncertainty modeling, exist. This contribution continues these researches by investigation of an existing fuzzy field concept. Based on discussion of limitations in the existing concept, novel developments in modeling and uncertainty quantification of fuzzy fields are presented. The developments are based on extending an existing interval dependency method, where multidimensional parallelepipeds characterize the underlying interval dependency. Therefore, a dependency model is formulated by extension from interval to fuzzy fields. The proposed (auto-)interaction concept is in analogy to the (auto-)correlation concept of random fields. It is demonstrated how an eigenvalue decomposition of the auto-interaction structure with reduced orthogonal basis variables can be implemented to reduce the high-dimensional α-level optimization problem in uncertainty quantification. Finally, the novel methods are validated by uncertainty quantification examples in benchmark functions to demonstrate the safety assessment capabilities.