Joint Random-Fuzzy Variables: A Tool for Propagating Uncertainty Through Nonlinear Measurement Functions

A still open issue, in uncertainty evaluation, is asymmetrical distributions of the values that can be attributed to the measurand. This problem generally becomes not negligible when the measurement function is highly nonlinear. In this case, the law of uncertainty propagation suggested by the Guide to the Expression of Uncertainty in Measurement is not correct any longer, and only Monte Carlo simulations can be used to obtain such distributions. This paper shows how this problem can be solved in a quite immediate way when measurement results are expressed in terms of random-fuzzy variables. Under this approach, nonrandom contributions to uncertainty can also be considered. An experimental example is reported and the results compared with those obtained by means of Monte Carlo simulations, showing the effectiveness of the proposed approach.