# Dempster-Shafer Belief function

This last week, my bioinformatics class was introduced to this Bayesian function (see http://www.blutner.de/uncert/DSTh.pdf for more).  What got me wondering was this measure:

Given an event frame A, you can measure the probabilities not just of each individual event, but each possible set of events as follows:

For every possible subset of A, $\latex Bel(A) = \sum_{B \subseteq A} = m(B)$

Now this looks like the beginnings of a Hopf algebra to me.  I ran it by the professor who was presenting, and he was intrigued but didn’t know the answer, although he mentioned one of his colleagues used posets in one of his papers on the mathematics of the Dempster-Shafer function.  Does it look like a possible Hopf algebra to you?  If so, do you think it would be useful to the probability behind the function?