Principle

Principle

The criterion allowing to determine which fusion to use is the height of the intersection of the various opinions expressed by each source. This height, which corresponds to a degree of consensus between the sources, is measured by the height of the intersection between the possibility distributions provided by each source.

Let us then note that the height h of the intersection of two possibility distributions $\pi_1$ and $\pi_2$ , defined onto the referential set $\Omega$ , is calculated as follows:

$\begin{displaymath}h(\pi_1, \pi_2) = \sup_{\omega \in \Omega} (\min(\pi_1(\omega), \pi_2(\omega)))\end{displaymath}$

(57)

A height of 1 means that the consensus is total between the sources; fusion will be then conjunctive.
A height of 0 states there is no agreement between the sources. Disjunctive fusion is used in this situation of total conflict.
A height between 0 and 1 means that there is a partial agreement, or a partial conflict, between the sources. In this case, the two kinds of fusion, conjunctive and disjunctive, are used, but disjunctive fusion is more or less limited according to the degree of consensus between the sources.

The rule of adaptive fusion is presented in paragraph ``Adaptive fusion''. Let us then briefly represent its behaviour.

The adaptive fusion of two sources S₁ and S₂ is defined as follows (figure 31):

$\begin{displaymath}\forall \omega \in \Omega, \quad\pi_{\text{ad}}(\omega) =\......{\min(1-h(\pi_1, \pi_2),\pi_{\text{disj}}(\omega))}} \right)\end{displaymath}$

(58)

**Figure 31:** Adaptive fusion of two sources in low conflict.
$\begin{figure}\begin{center}\epsfbox{c3-ad3.eps}\end{center}\end{figure}$

Part A of the rule corresponds to renormalized conjunctive fusion. It is used when the sources are in agreement (areas where the distributions $\pi_1$ and $\pi_2$ have an intersection).
Part B corresponds to the disjunctive fusion used in the case of conflict between the sources. The importance attached to this disjunctive fusion varies from 1 (when the conflict is total) to 0 (when the agreement is total).

This rule was defined to perform the fusion of only two sources.

IRIT-UPS