Uncertainty modeling of random and systematic errors by means of Monte Carlo and fuzzy techniques

The standard reference in uncertainty modeling is the ‘‘Guide to the Expression of Uncertainty in Measurement (GUM)’’. GUM groups the occurring uncertain quantities into ‘‘Type A’’ and ‘‘Type B’’. Uncertainties of ‘‘Type A’’ are determined with the classical statistical methods, while ‘‘Type B’’ is subject to other uncertainties which are obtained by experience and knowledge about an instrument or a measurement process. Both types of uncertainty can have random and systematic error components. Our study focuses on a detailed comparison of probability and fuzzy-random approaches for handling and propagating the di¤erent uncertainties, especially those of ‘‘Type B’’. Whereas a probabilistic approach treats all uncertainties as having a random nature, the fuzzy technique distinguishes between random and deterministic errors. In the fuzzy-random approach the random components are modeled in a stochastic framework, and the deterministic uncertainties are treated by means of a range-of-values search problem. The applied procedure is outlined showing both the theory and a numerical example for the evaluation of uncertainties in an application for terrestrial laserscanning (TLS).