Modeling and Processing Measurement Uncertainty within the Theory of Evidence: Mathematics of Random-Fuzzy Variables

Random–fuzzy variables (RFVs) are mathematical variables defined within the theory of evidence. Their importance in measurement activities is due to the fact that they can be employed for the representation of measurement results, together with the associated uncertainty, whether its nature is random effects, systematic effects, or unknown effects. Of course, their importance and usability also depend on the fact that they can be employed for processing measurement results. This paper proposes suitable mathematics and related calculus for processing RFVs, which consider the different nature and the different behavior of the uncertainty effects. The proposed approach yields to process measurement algorithms directly in terms of RFVs so that the final measurement result (and all associated available information) is provided as an RFV.