  In this work, we will analyze a noncommutative (NC) version of the
Friedmann-Robert-Walker cosmological models within the gravitational
Ho\v{r}ava-Lifshitz theory. The matter content of the models is described by a
perfect fluid and the constant curvature of the spatial sections may be
positive, negative or zero. In order to obtain this theory, we will use the
Faddeev-Jackiw symplectic formalism to introduce, naturally, space-time
noncommutativity inside the equations that provide the dynamics of the theory.
We will investigate, in details, the classical field equations of a particular
version of the NC models. The equations will be modified, with respect to the
commutative ones, by the introduction of a NC parameter. We will demonstrate
that various NC models, with different types of matter and spatial constant
curvatures, show several interesting and new results relative to the
corresponding commutative ones. We will pay special attention to some cases,
where the NC model predicts a scale factor accelerated expansion, which may
describe the current state of our Universe.
