The random-fuzzy variables: A new approach for the expression of uncertainty in measurement

The IEC-ISO Guide to the expression of uncertainty in measurement provides the definition of the uncertainty of a measurement result and the guidelines to estimate express and process it. The guide refers to the probability theory, as the most known and used mathematical tool to deal with distributions of values. However, the probability theory is not the only tool to deal with distributions of values and is not the most suitable one when the values do not distribute in a totally random way. A more general theory, the theory of the evidence should be considered that encompasses the probability theory and the possibility theory. This paper recalls the fundamentals of the theory of the evidence and shows how the random-fuzzy variables can be framed within this theory and usefully employed to represent the result of a measurement together with its associated uncertainty. Mathematics is defined on the random-fuzzy variables, so that the uncertainty can be processed and simple examples are given showing the effectiveness of these variables in expressing the result of a measurement and its uncertainty in full agreement with the spirit of the IEC-ISO Guide.