On an Interval-Valued Solution of the Marginal Problem

In the 1980s, a version of a marginal problem considered in this paper was connected, with the necessity to cope with a task of knowledge integration in probabilistic expert systems. In practical situations, marginal distributions representing pieces of local knowledge are often inconsistent. The present paper introduces an interval-valued solution, which always exists, of a marginal problem even in cases when, because of inconsistencies one cannot get a solution in a classical sense. This paper shows how the famous Iterative Proportional Fitting Procedure, which is often used to get a classical solution of a consistent problem, can also be exploited when constructing an interval-valued solution, and how any solution can be improved (tightened).