  In this paper we generalize the fermionic representation for $S=1/2$ spins to
arbitrary spins. Within a mean field theory we obtain several spin liquid
states for spin $S=1$ antiferromagnets on triangular lattices, including
gapless f-wave spin liquid and topologically nontrivial $p_x+ip_y$ spin liquid.
After considering different competing orders, we construct a phase diagram for
the $J_1$-$J_3$-$K$ model. The application to recently discovered material
$\mathrm{NiGa_2S_4}$ is discussed.
