Lp consonant approximation of belief functions in the mass space

In this paper we pose the problem of approximating an arbitrary belief function (b.f.) with a consonant one, in a geometric framework in which belief functions are represented by the vectors of their basic probabilities, or “mass space”. Given such a vector ~ mb, the consonant b.f. which minimizes an appropriate distance function from ~ mb can be sought. We consider here the classical L1, L2 and Lp norms. As consonant belief functions live in a collection of simplices in the mass space, partial approximations on each individual simplex have to be computed in order to find the overall approximation. Interpretations of the obtained approximations in terms of basic probabilities are proposed, and the results compared with those of previous approaches, in particular outer consonant approximation.