From Relations Between Sets to Relations Between Belief Functions

In uncertainty theories, a common problem is to define how we can extend relations between sets (e.g., inclusion, ranking, consistency,...) to corresponding notions between uncertainty representations. Such definitions can then be used to perform the same operations as those that are done for sets: measuring information content, ordering alternatives or checking consistency, to name a few. In this paper, we propose a general way to extend set relations to belief functions, using constrained stochastic matrices to identify those belief functions in relation. We then study some properties of our proposal, as well as its relations with existing works focusing on peculiar relations.