Plausibility function ($\mathrm{Pl}$)

The plausibility function associated with a finite basic probability assignment $m$ isIt includes all evidence that does not exclude $A$, whereas the belief function includes only support wholly committed to $A$. Consequently $\mathrm{Bel}(A)\le \mathrm{Pl}(A)$.

For $m(\{r\})=0.6$ and $m(\{r,b\})=0.4$, $\mathrm{Pl}(\{r\})=1$ and $\mathrm{Pl}(\{b\})=0.4$. Their sum exceeds one, so these are not the two probabilities of an ordinary binary probability distribution. In the random-subset interpretation, $\mathrm{Pl}(A)=\mathbb{P}(S\cap A\ne \varnothing )$: some possibility in $A$ remains compatible with the evidence. The gap from the belief function measures how much support remains unresolved with respect to $A$.^[ref]