A metrology-sound probability-possibility transformation for joint distributions

In the recent years the possibility theory has been investigated by many Authors in the field of mathematics and engineering. A possibility distribution is, from the mathematical point of view, a generalization of a probability distribution, since it can represent a family of probability distributions. Given a probability distribution, different probability-possibility transformations have been defined, which transform the probability distribution into different possibility distributions. Probability-possibility transformations are useful in any problem where statistical data must be dealt within the possibility theory, together with other heterogeneous uncertain and imprecise data. This paper generalizes these transformations to two-dimensional distributions with a particular care to the maximum specificity principle, so that joint probability distributions can be suitably transformed into maximally specific joint possibility distributions.