### Fabio Cuzzolin

## Lp consonant approximation of belief functions in the mass space

### Abstract

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.

### Keywords

Consonant belief functions, (outer) consonant approximation, geometric approach, mass space, Lp norms.

### Download area

The paper is available in the following formats:

### Authors’ addresses

Department of Computing

Oxford Brookes University

Wheatley campus

OX33 1HX

Oxford

### E-mail addresses