The Construction of Joint Possibility Distributions of Random Contributions to Uncertainty

The evaluation and expression of uncertainty in measurement is one of the fundamental issues in measurement science and challenges measurement experts especially when the combined uncertainty has to be evaluated. Recently, a new approach, within the framework of possibility theory, has been proposed to generalize the currently followed probabilistic approach. When possibility distributions are employed to represent random contribution to measurement uncertainty, their combination is still an open problem. This combination is directly related to the construction of the joint possibility distribution, generally performed by means of t-norms. The problem is that joint possibility distributions strongly depend on the considered t-norm, and, therefore, the choice of one particular t-norm over another has to be justified. The first goal of this paper is, hence, to provide support to the choice of a particular t-norm. The second goal is to discuss the construction of the joint possibility distribution when the two random contributions to uncertainty show mutual dependence, with specific reference to a particular class of possibility distributions.