Presentation of the method

Presentation of the Method

Dubois and Prade defined a criterion to determine whether sources agree or not, and thus to choose which type of fusion to apply.

Let $\pi_1$ and $\pi_2$ be the possibility distributions given by sources 1 and 2 relative to the value of parameter x.

The criterion selected is the height $h(\pi_1, \pi_2)$ of the intersection of the possibility distributions provided by each source, noted consensus degree. Height $h(\pi_1, \pi_2)$ denotes the degree of certainty of the reliability of two sources:

If $h(\pi_1, \pi_2) = 1$ , the sources are reliable as their possibility distributions overlap largely. There is no conflict. It is a favourable context for the use of conjunctive fusion.
When $h(\pi_1, \pi_2) < 1$ , there is some conflict. The lower the degree of consensus, h, the stronger the conflict is.
In order to take the conflict into account, the two modes of fusion, conjunctive and disjunctive, are applied in parallel. The importance given to each one depends on h. Finally when h becomes null, conflict is total between the sources. Only disjunctive fusion is then applicable.

The rule for adaptive fusion is the following:

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

(56)

It can be split into two parts.

Part A is a renormalized conjunctive fusion. This part is used when the sources agree $(0 < h(\pi_1, \pi_2) \leqslant 1)$ .
Part B is used in disjunctive fusion $\pi_{\text{disk}}(\omega)$ . Nevertheless, it is limited by the amount of conflict between sources i.e. $1 - h(\pi_1, \pi_2)$ . This limitation allows a switch from conjunctive-style fusion to disjunctive-style fusion according to the value of h. Moreover, disjunctive fusion is limited to favour the assumption that the two sources are reliable.

IRIT-UPS