The mathematical theory of evidence and measurement uncertainty - Expression and combination of measurement results via the random-fuzzy variables

In a previous paper [1], it was proved how total ignorance can be effectively represented, in Shafer's theory of evidence [2], by a rectangular possibility distribution. In addition, it was shown how this concept can be usefully employed to mathematically represent situations that are often met in the measurement practice, especially in the industrial world [3]. The aim of this new paper is to show how possibility distributions can be effectively used to represent any kind of knowledge, from total ignorance to total evidence, and combine different contributions, if necessary.