Belief Function Theory - Information Fusion in Signal and Image Processing - page 108

In particular, the intervals [Bel , Pls] are reduced after the combination, since the
mass functions are more focused than the initial masses (they pertain to smaller sets).

On the other hand, the mass on the empty set (which measures conflict) increases
during fusion.

Let us now assume that the model partly includes the absence of knowledge and
that a non-zero mass is assigned to D in both sources. We then get the following
intersection table:

C 1 ∪ C 2 C 3 D

C 1 C 1 ∅ C 1

C 2 ∪ C 3 C 2 C 3 C 2 ∪ C 3

D C 1 ∪ C 2 C 3 D

This time, the ambiguity is only partially reduced and non-zero mass remains on
the imprecise elements (class disjunction). The conflict, on the other hand, is dimin-
ished, which is a property that is true in general of the combination of weakened
masses by reinforcing D .

7.4.4. Discounting

Discounting allows us to model the reliability of the sources with the help of a
coefficient α ( α

[0 , 1]) used for increasing the mass on D . The idea is to strengthen
the absence of knowledge as the source becomes less reliable. A mass function m is
then transformed into a mass function m according to the following formulae:

∈

m ( A )= αm ( A ) ∀ A, A = D,

α 1 m ( D ) =1 m ( D )=1

− − − α + αm ( D ) .

The effect of discounting is to increase the intervals [Bel , Pls] and, during the
combination, to reduce conflict.

7.4.5. Conditioning

We now consider the specific case of a source that provides a certain element of
information on a subset B of D . This information is modeled as follows:

m B ( B )=1and ∀ A ⊆ D, A = B, m B ( A )=0 . [7.30]