The Transferable Belief Model and Other Interpretations of\n Dempster-Shafer's Model

Dempster-Shafer's model aims at quantifying degrees of belief But there are\nso many interpretations of Dempster-Shafer's theory in the literature that it\nseems useful to present the various contenders in order to clarify their\nrespective positions. We shall successively consider the classical probability\nmodel, the upper and lower probabilities model, Dempster's model, the\ntransferable belief model, the evidentiary value model, the provability or\nnecessity model. None of these models has received the qualification of\nDempster-Shafer. In fact the transferable belief model is our interpretation\nnot of Dempster's work but of Shafer's work as presented in his book (Shafer\n1976, Smets 1988). It is a ?purified' form of Dempster-Shafer's model in which\nany connection with probability concept has been deleted. Any model for belief\nhas at least two components: one static that describes our state of belief, the\nother dynamic that explains how to update our belief given new pieces of\ninformation. We insist on the fact that both components must be considered in\norder to study these models. Too many authors restrict themselves to the static\ncomponent and conclude that Dempster-Shafer theory is the same as some other\ntheory. But once the dynamic component is considered, these conclusions break\ndown. Any comparison based only on the static component is too restricted. The\ndynamic component must also be considered as the originality of the models\nbased on belief functions lies in its dynamic component.\n