Independence concepts in evidence theory

We study three conditions of independence within Evidence Theory framework. First condition refers to the selection of pairs of focal sets. The remaining two are related to the choice of a pair of elements, once a pair of focal sets has been selected. These three concepts allow us to formalize the ideas of lack of interaction between variables and between their (imprecise) observations. We illustrate the difference between both types of independence with simple examples about drawing balls from urns. We show that there are not implication relationships between both of them. We derive interesting conclusions about the relationships between the concepts of "independence in the selection" and "random set independence".