Uncertainty evaluation for complex propagation models by means of the theory of evidence

The present paper describes operating procedures for uncertainty expression and propagation using different approaches. Well-known methods, such as the propagation formula of the GUM (Guide to the Expression of Uncertainty in Measurement) and Monte Carlo method, are briefly described and summarized as operating procedures, while a more detailed description of the new approach based on the theory of evidence and random-fuzzy variables (RFVs) is presented. This new method based on RFV allows us to take into explicit account and to properly manage systematic effects and complete ignorance contributions to uncertainty. For all three methods, concise and schematic procedures are presented in order to give a clear comparison among them and to ease implementation. Particular attention is focused on how uncertainty can be expressed and propagated in an indirect measurement through a mathematical model. Furthermore, this paper proposes a generalized method to express and propagate uncertainty by means of RFV. This proposed method is characterized by its applicability to any type of mathematical model, even if it comprises complex numerical functions or algorithms.