A possibilistic marginal problem is introduced in a way analogous to probabilistic framework, to address the question of whether or not a common extension exists for a given set of marginal distributions. Similarities and differences between possibilistic and probabilistic marginal problems will be demonstrated, concerning necessary condition and sets of all solutions. The operators of composition will be recalled and we will show how to use them for finding a T-product extension. Finally, a necessary and sufficient condition for the existence of a solution will be presented.
In contrast to most other approaches used to represent multidimensional probability distributions, which are based on graphical Markov modelling (i.e. dependence structure of distributions is represented by graphs), the described method is rather procedural. Here, we describe a process by which a multidimensional distribution can be composed from a “generating sequence” - a sequence of low-dimensional distributions. The main advantage of this approach is that the same apparatus based on operators of composition can be applied for description of both probabilistic and possibilistic models.