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Dempster's Rule of Combination


Dempster's rule allows aggregation of two different bodies of evidence $(\mathcal{F}_1, m_1)$ and $(\mathcal{F}_2, m_2)$ on the same reference set.

We can imagine that several experts indicate their opinion via the attribution of masses of belief m1 and m2 over $\Omega$, or that two successive experiments allow such an attribution.

Dempster's rule of combination highlights combined masses of belief in the following way:

\begin{displaymath}m_{12}(A) = \frac{\sum_{B \subseteq \Omega, \; C \subseteq \O......bseteq \Omega, \; B \cap C = \varnothing} m_1(B) \cdot m_2(C)}\end{displaymath}
(82)


The denominator is a coefficient of normalization. In particular, if it is null, it means that there is a total conflict between the sources, and aggregation is then impossible.

The use of this rule is thus valid only when the sources are sufficiently in agreement. This operator is unstable when the conflict is very strong, as shown by [Zadeh, 1984] (see also [Smets, 1990]).





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