On Two Composition Operators in Dempster-Shafer Theory

Efficient computations with probabilistic multidimensional models are made possible if the respective probability measure (distribution) is in the form of a decomposable model. Some of the advantageous properties of these models are based on the fact that factorization and conditional independence coincide. It means that a decomposable multidimensional model can be assembled (composed) from its low-dimensional marginals with the help of an operator of composition, which introduces conditional independence relations among the variables. The problem arises when we also want to apply these ideas in Dempster-Shafer theory of evidence, because two different operators of composition have been introduced in literature. The present paper serves as a survey of results on these two operators, recollects their common properties and differences, and tries to find a proper role for each of them.