  We introduce a category $\widehat{\mathcal{O}}_{\rm osc}$ of $q$-oscillator
representations of the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_n)$.
We show that $\widehat{\mathcal{O}}_{\rm osc}$ has a family of irreducible
representations, which naturally corresponds to finite-dimensional irreducible
representations of quantum affine algebra of untwisted affine type $A$. It is
done by constructing a category of $q$-oscillator representations of the
quantum affine superalgebra of type $A$, which interpolates these two family of
irreducible representations. The category $\widehat{\mathcal{O}}_{\rm osc}$ can
be viewed as a quantum affine analogue of the semisimple tensor category
generated by unitarizable highest weight representations of
$\mathfrak{gl}_{u+v}$ ($n=u+v$) appearing in the
$(\mathfrak{gl}_{u+v},\mathfrak{gl}_\ell)$-duality on a bosonic Fock space.
