On the interrelation between Dempster–Shafer Belief Structures and their Belief Cumulative Distribution Functions

We consider Dempster–Shafer belief structures (DSBSs) mm having finitely many non-empty compact intervals as focal elements and prove several results describing the interrelation between DSBSs and their so-called Belief Cumulative Distribution Functions (BCDFs) x↦F(x)=(F̲(x),F¯(x)) induced by the corresponding belief and plausibility measures. In particular, we answer a question by Ronald R. Yager on the injectivity of the assignment m↦F.