A Note on Factorization of Belief Functions

Practically all methods for efficient computation with multidimensional models take advantage of the fact that the model in question in a way factorizes. It means that it is possible to decompose the model into its low-dimensional parts, each of which can be defined with a reasonable number of parameters. This is a basic idea of computation with probabilistic Graphical Markov Models as well as with belief or credal networks. For belief functions, two types of factorization were designed in the literature: one is based on the famous Dempster’s rule of combination, the other uses an operator of composition. The paper compares these two types of factorization, shows that both the approaches are equivalent to each other in case of unconditional factorization and shows what are the differences when overlapping factorization is studied.