A fuzzy-based approach to comprehensive modeling and analysis of systems with epistemic uncertainties

While aleatory uncertainties have successfully been taken into account by the use of probability theory, the modeling of epistemic uncertainties still remains a challenging topic. As a practical approach to solve this limitation, an interdisciplinary methodology to comprehensive modeling and analysis of systems is presented, which allows for the inclusion of uncertainties – in particular of those of epistemic type – from the very beginning of the modeling procedure. This approach is based on fuzzy arithmetic, a special field of fuzzy set theory, which has gained practical relevance after the introduction of the so-called Transformation Method. As practical and illustrative examples of two different areas of the engineering sciences, the fuzzy arithmetical approach to comprehensive modeling and analysis of uncertain systems is applied to the simulation of automotive crash in structural dynamics as well as to the simulation of landslide failure in geotechnical science and engineering. In both applications, epistemic uncertainties are considered which arise from some lack of knowledge, from simplification in modeling as well as from subjectivity in implementation.