On Random Sets Independence and Strong Independence in Evidence Theory

摘要

Belief and plausibility functions can be viewed as lower and upper probabilities possessing special properties. Therefore, (conditional) independence concepts from the framework of imprecise probabilities can also be applied to its sub-framework of evidence theory. In this paper we concentrate ourselves on random sets independence, which seems to be a natural concept in evidence theory, and strong independence, one of two principal concepts (together with epistemic independence) in the framework of credal sets. We show that application of strong independence to two bodies of evidence generally leads to a model which is beyond the framework of evidence theory. Nevertheless, if we add a condition on resulting focal elements, then strong independence reduces to random sets independence. Unfortunately, it is not valid no more for conditional independence.