  We obtain the Kerr-anti-de-sitter (Kerr-AdS) and Kerr-de-sitter (Kerr-dS)
black hole (BH) solutions to the Einstein field equation in the perfect fluid
dark matter background using the Newman-Janis method and Mathematica package.
We discuss in detail the black hole properties and obtain the following main
results: (i) From the horizon equation $g_{rr}=0$, we derive the relation
between the perfect fluid dark matter parameter $\alpha$ and the cosmological
constant $\Lambda$ when the cosmological horizon $r_{\Lambda}$ exists. For
$\Lambda=0$, we find that $\alpha$ is in the range $0<\alpha<2M$ for $\alpha>0$
and $-7.18M<\alpha<0$ for $\alpha<0$. For positive cosmological constant
$\Lambda$ (Kerr-AdS BH), $\alpha_{max}$ decreases if $\alpha>0$, and
$\alpha_{min}$ increases if $\alpha<0$. For negative cosmological constant
$-\Lambda$ (Kerr-dS BH), $\alpha_{max}$ increases if $\alpha>0$ and
$\alpha_{min}$ decreases if $\alpha<0$; (ii) An ergosphere exists between the
event horizon and the outer static limit surface. The size of the ergosphere
evolves oppositely for $\alpha>0$ and $\alpha<0$, while decreasing with the
increasing $\mid\alpha\mid$. When there is sufficient dark matter around the
black hole, the black hole spacetime changes remarkably; (iii) The singularity
of these black holes is the same as that of rotational black holes. In
addition, we study the geodesic motion using the Hamilton-Jacobi formalism and
find that when $\alpha$ is in the above ranges for $\Lambda=0$, stable orbits
exist. Furthermore, the rotational velocity of the black hole in the equatorial
plane has different behaviour for different $\alpha$ and the black hole spin
$a$. It is asymptotically flat and independent of $\alpha$ if $\alpha>0$ while
is asymptotically flat only when $\alpha$ is close to zero if $\alpha<0$.
