Approximation of Belief Functions by Minimizing Euclidean Distances

This paper addresses the approximation of belief functions by minimizing the Euclidean distance to a given belief function in the set of probability functions. The special case of Dempster-Shafer belief functions is considered in particular detail. It turns out that, in this case, an explicit solution by means of a projective transformation can be given. Furthermore, we also consider more general concepts of belief. We state that the approximation by means of minimizing the Euclidean distance, unlike other methods that are restricted to Dempster-Shafer belief, works as well. However, the projective transformation formula cannot necessarily be applied in these more general settings.