  We formulate a viable low-scale seesaw model, where the masses for the
standard model (SM) charged fermions lighter than the top quark emerge from a
universal seesaw mechanism mediated by charged vectorlike fermions. The small
light active neutrino masses are produced from an inverse seesaw mechanism
mediated by right-handed Majorana neutrinos. Our model is based on the $A_{4} $
family symmetry, supplemented by cyclic symmetries, whose spontaneous breaking
produces the observed pattern of SM fermion masses and mixings. The model can
accommodate the muon and electron anomalous magnetic dipole moments and
predicts strongly suppressed $\mu\rightarrow e\gamma $ and $\tau\rightarrow \mu
\gamma $ decay rates, but allows a $\tau \rightarrow e\gamma $ decay within the
reach of the forthcoming experiments.
