Fuzzy, probabilistic and stochastic modelling of an elastically bedded beam

This article sets out to compare the effects of modelling uncertainty using fuzzy sets, random variables and stochastic analysis. With the aid of an example from civil engineering - the bending equation for an elastically bedded beam - we discuss what each model is or is not capable of capturing. All models may be adequately used for variability studies, but may fail to detect the effect of localized parameter fluctuations on the response of the system. In the stochastics setting, we show an instance of the linearization effect of large noise which says that under large stochastic excitations, the contributions of nonlinear terms may be annihilated.