  By analyzing 482 pb$^{-1}$ of $e^+e^-$ collision data collected at the
center-of-mass energy $\sqrt s=4.009$ GeV with the BESIII detector, we measure
the %absolute branching fractions for the semi-leptonic decays $D_{s}^{+}\to
\phi e^{+}\nu_{e}$, $\phi \mu^{+}\nu_{\mu}$, $\eta \mu^{+}\nu_{\mu}$ and
$\eta'\mu^{+}\nu_{\mu}$ to be ${\mathcal B}(D_{s}^{+}\to\phi
e^{+}\nu_{e})=(2.26\pm0.45\pm0.09)$\%, ${\mathcal B}(D_{s}^{+}\to\phi
\mu^{+}\nu_{\mu})=(1.94\pm0.53\pm0.09)$\%, ${\mathcal B}(D_{s}^{+}\to\eta
\mu^{+}\nu_{\mu})=(2.42\pm0.46\pm0.11)$\% and ${\mathcal
B}(D_{s}^{+}\to\eta'\mu^{+} \nu_{\mu}) = (1.06\pm0.54\pm0.07)$\%, where the
first and second uncertainties are statistical and systematic, respectively.
The branching fractions for the three semi-muonic decays $D_s^+\to\phi
\mu^+\nu_\mu, \eta \mu^+\nu_\mu$ and $\eta' \mu^+\nu_\mu$ are determined for
the first time and that of $D^+_s\to \phi e^+\nu_e$ is consistent with the
world average value within uncertainties.
