Certainly uncertain - the charm of fuzzy predictions

Abstract A common problem in the numerical simulation of complex real-world systems is the fact that the parameters of the models usually exhibit some degree of uncertainty and exact values for their quantification can hardly be provided. This non-determinism in numerical models may arise as a consequence of different sources: on the one hand, natural variability or scatter, on the other hand, uncertainties that arise from an absence of information, vagueness in parameter definition, subjectivity in numerical implementation, or simplification and idealization as it usually appears in every modeling procedure. As one possible approach to solve this limitation, an interdisciplinary methodology to an advanced modeling and analysis of systems is presented, which allows for the inclusion of uncertainties from the very beginning of the modeling procedure. This approach is based on fuzzy arithmetic, a special field of fuzzy set theory, where the uncertain values of the model parameters are represented by so-called fuzzy numbers, reflecting in a rather intuitive and plausible way the blurred range of possible parameter values. As a result of this special modeling technique, more comprehensive system models can be derived which outperform the conventional, crisp-parameterized models by providing simulation results which reflect both the system dynamics and the effect of the uncertainties. The methodology is exemplarily illustrated by an application from the field of automotive crash simulation which demonstrates that advanced modeling and simulation of dynamical systems, based on fuzzy arithmetical techniques for including the presumably limiting uncertainties, can provide significant additional benefit. A variety of further applications from other fields of the engineering sciences is given in the references, highlighting the charm of fuzzy predictions.