Consonant approximations of belief functions

$L_{p}$ Consonant Approximations of Belief Functions

In this paper we solve the problem of approximating a belief measure with a necessity measure or “consonant belief function” in a geometric framework. Consonant belief functions form a simplicial complex in both the space of all belief functions and the space of all mass vectors: partial approximations are first sought in each component of the complex, while global solutions are selected among ...

Consonant approximations of belief functions on the consonant simplex

1 The consonant approximation problem Given a belief function b ∈ B and a sub-class of b.f.s A, the problem consists on finding the function a ∈ A which the " closest " to b, according to some criterion (for instance by minimizing a certain distance function d(a, b)). 1.1 Previous solutions 1.2 Paper outline 2 Geometry of consonant belief functions 2.1 Consonant belief functions The theory of e...

Consonant Approximations in the Belief Space

In this paper we solve the problem of approximating a belief measure with a necessity measure or “consonant belief function” by minimizing appropriate distances from the consonant complex in the space of all belief functions. Partial approximations are first sought in each simplicial component of the consonant complex, while global solutions are obtained from the set of partial ones. The L1, L2...

Faithful Approximations of Belief Functions

A conceptual foundation for approximation of belief functions is proposed and investi­ gated. It is based on the requirements of consistency and closeness. An optimal ap­ proximation is studied. Unfortunately, the computation of the optimal approximation turns out to be intractable. Hence, various heuristic methods are proposed and exper­ imantally evaluated both in terms of their accuracy and ...

Coarsening Approximations of Belief Functions