  The compatibility of quantitative and qualitative representations of beliefs
was studied extensively in probability theory. It is only recently that this
important topic is considered in the context of belief functions. In this
paper, the compatibility of various quantitative belief measures and
qualitative belief structures is investigated. Four classes of belief measures
considered are: the probability function, the monotonic belief function,
Shafer's belief function, and Smets' generalized belief function. The analysis
of their individual compatibility with different belief structures not only
provides a sound b<msis for these quantitative measures, but also alleviates
some of the difficulties in the acquisition and interpretation of numeric
belief numbers. It is shown that the structure of qualitative probability is
compatible with monotonic belief functions. Moreover, a belief structure
slightly weaker than that of qualitative belief is compatible with Smets'
generalized belief functions.
