  Based on the well-known cardinal characteristics $\mathfrak{s}$,
$\mathfrak{r}$ and $\mathfrak{i}$, we introduce nine related cardinal
characteristics by using the notion of asymptotic density to characterise
different intersection properties of infinite sets. We prove several bounds and
consistency results, e. g. the consistency of $\mathfrak{s} <
\mathfrak{s}_{1/2}$, as well as several results about possible values of
$\mathfrak{i}_{1/2}$.
