Compositional models and conditional independence in evidence theory

The goal of the paper is twofold. The first is to show that some of the ideas for representation of multidimensional distributions in probability and possibility theories can be transferred into evidence theory. Namely, we show that multidimensional basic assignments can be rather efficiently represented in a form of so-called compositional models. These models are based on the iterative application of the operator of composition, whose definition for basic assignments as well as its properties are presented. We also prove that the operator of composition in evidence theory is in a sense generalization of its probabilistic counterpart.The second goal of the paper is to introduce a new definition of conditional independence in evidence theory and to show in what sense it is superior to that formerly introduced by other authors.