On Modeling Uncertainty in Input and Output Data

Almost all (if not all) models are burdened with uncertainty. Even if we set aside the difficulties in choosing the adequate level and complexity of a mathematical model, the problem of uncertainty in the numerical values of input parameters is omnipresent. In civil or mechanical engineering, for instance, the knowledge of material parameters is essential. Their numerical values can be found in handbooks but, usually, only as crisp numbers without details about their origin. Some basic statistical features (as histograms or standard deviations) of the fundamental material parameters can be found in extensive or specialized handbooks, but these are hardly available to ordinary analysts.