Geometric analysis of belief space and conditional subspaces.
Fabio Cuzzolin, R. Frezza · 2001
In this paper the geometric structure of the space S of the belief functions dened over a discrete set (be- lief space) is analyzed. Using the Moebius inversion lemma we prove the recursive bundle structure of the belief space and show how an arbitrary belief function can be uniquely represented as a convex combination of certain elements of the bers, giving S the form of a simplex. The commutativity of orthogonal sum and convex closure operator is proved and used to depict the geometric structure of conditional subspaces, i.e. sets of belief functions conditioned by a given function s. Future applications of these geometric methods to classical problems like probabilistic approximation and canonical decomposition are outlined.