= Basic probability assignment
{title2=$m$}
On a finite <sample space> $\Theta$, a <basic probability assignment> in <Dempster-Shafer theory> is a <function> on its <power set> satisfying
$$
m(\varnothing)=0,\qquad m(B)\ge0,\qquad\sum_{B\subseteq\Theta}m(B)=1.
$$
The mass $m(B)$ is support committed to $B$ as a whole, without allocating it among the elements of $B$. Thus $m$ is a <probability distribution> over subsets, and generally is not an additive <probability measure> on $\Theta$.
For $\Theta=\{r,b\}$, let $m(\{r\})=0.6$ and $m(\Theta)=0.4$. The second mass expresses unresolved support between $r$ and $b$; it is not a claim that $b$ has <probability> $0.4$. This assignment induces <belief function> value $0.6$ and <plausibility function> value one for $\{r\}$. Ordinary additive <probability> is recovered when all nonzero masses are on singleton subsets.<Belief Functions: Introduction by Glenn Shafer>[Sections 1–2, evidence committed to sets and uncommitted belief]{ref}
Back to article page
