Many authors have studied fuzzy belief structures, that is belief functions having fuzzy sets as focal elements. One of the main reason for this is that this structure offers a convenient way to mix probabilistic and fuzzy information. Still, one point on which authors often disagree is how information represented by fuzzy belief structures should be processed, i.e., how should be defined fusion operations, decision rules, uncertainty measures, uncertainty propagation, etc. for such representations. In this paper, we consider that fuzzy belief structures are mapped into classical belief structures encoding the same information, and propose to manipulate these latter structures. From a practical standpoint, it has the benefit that processing tools proper to belief structures can be used together with their interpretation, rather than having to consider a mix of probabilistic and fuzzy calculi, which can be harder to interpret