= Plausibility function
{title2=$\operatorname{Pl}$}
The <plausibility function> associated with a finite <basic probability assignment> $m$ is
$$
\operatorname{Pl}(A)=\sum_{B\cap A\ne\varnothing}m(B)=1-\operatorname{Bel}(A^c).
$$
It includes all evidence that does not exclude $A$, whereas the <belief function> includes only support wholly committed to $A$. Consequently $\operatorname{Bel}(A)\le\operatorname{Pl}(A)$.
For $m(\{r\})=0.6$ and $m(\{r,b\})=0.4$, $\operatorname{Pl}(\{r\})=1$ and $\operatorname{Pl}(\{b\})=0.4$. Their sum exceeds one, so these are not the two probabilities of an ordinary binary <probability distribution>. In the random-subset interpretation, $\operatorname{Pl}(A)=\mathbb P(S\cap A\ne\varnothing)$: some possibility in $A$ remains compatible with the evidence. The gap from the <belief function> measures how much support remains unresolved with respect to $A$.<Belief Functions: Introduction by Glenn Shafer>[Sections 1–2, lower and upper degrees of support]{ref}
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