Independence concepts in evidence theory: some results about epistemic irrelevance and imprecise belief functions

Many extensions of classical stochastic independence have been proposed when working with probability sets to represent uncertainty. As belief functions can be seen as particular instances of such probability sets, some authors have investigated how these extensions can be reinterpreted and retrieved in the particular framework of belief functions. They have mainly focused on the so-called notions of random set independence, fuzzy non-interaction, strong independence and unknown interaction. In this paper, we pursue this effort in two ways: first by showing that the notion of epistemic irrelevance, central in Walley theory of lower previsions, can be likewise reinterpreted in terms of belief functions; second by considering the more general case where mass assignments inducing belief functions are themselves imprecise.