Belief function and sub-sigma classes

 

Consider a discrete variable x with a finite set of values x. Suppose we impose a probability distribution m(A) into subsets of x. A belief function can be defined from the basic mass assignment as Bel(A) = sum_{B subA} m(B) [34]; the belief function is the convex set of distributions such that p(A) geBel(A) for all A. To generate the finitely many vertices of the credal set, we must concentrate the non-zero basic mass assignments into each one of their subsets, one at a time.

Consider a variable x with values x, and a specification of probabilities masses for non-overlapping subsets of x. This procedure characterizes a sub-class of the belief function class, called a sub-sigma class [3, 24, 28].