On interpretation of T-product extensions of possibility distributions

T-product extensions (where T is a continuous t-norm) of a system of low-dimensional possibility distributions form an important class of solutions of the so-called possibilistic marginal problem. Nevertheless, they can differ from each other, e.g., from the viewpoint of inference. Therefore the need for their interpretation is obvious. To find it, we identify any possibility distribution with a set of probability distributions dominated by it and find a probability interpretation of models based on Gödel's, product and Łukasiewicz's t-norms.