Conditional independence and factorization of multidimensional models

In this paper, three different frameworks for uncertainty description are considered: probability and possibility theories, and Dempster-Shafer theory of belief functions. For all of them special operators of composition are introduced, which enable, among others, defining the concept of factorization (used here as an alternative notion for conditional independence) meeting all the semigraphoid axioms. It is showed that whilst for probability and possibility theories factorization and conditional independence coincide, they differ from each other for belief functions. Since the introduced factorization manifests most of the properties required for the concept of conditional independence, the question arises whether it would be useful to substitute the often used concept of the conditional independence with the factorization introduced in this paper.