  Dempster-Shafer's model aims at quantifying degrees of belief But there are
so many interpretations of Dempster-Shafer's theory in the literature that it
seems useful to present the various contenders in order to clarify their
respective positions. We shall successively consider the classical probability
model, the upper and lower probabilities model, Dempster's model, the
transferable belief model, the evidentiary value model, the provability or
necessity model. None of these models has received the qualification of
Dempster-Shafer. In fact the transferable belief model is our interpretation
not of Dempster's work but of Shafer's work as presented in his book (Shafer
1976, Smets 1988). It is a ?purified' form of Dempster-Shafer's model in which
any connection with probability concept has been deleted. Any model for belief
has at least two components: one static that describes our state of belief, the
other dynamic that explains how to update our belief given new pieces of
information. We insist on the fact that both components must be considered in
order to study these models. Too many authors restrict themselves to the static
component and conclude that Dempster-Shafer theory is the same as some other
theory. But once the dynamic component is considered, these conclusions break
down. Any comparison based only on the static component is too restricted. The
dynamic component must also be considered as the originality of the models
based on belief functions lies in its dynamic component.
