  Recently, some theoretical models predicted that a small fraction of fast
radio bursts (FRBs) could be associated with gravitational waves (GWs). In this
work, we discuss the possibility of using GW/FRB association systems, if
commonly detected in the future, as a complementary cosmic probe. We propose
that upgraded standard sirens can be constructed from the joint measurements of
luminosity distances $D_{L}$ derived from GWs and dispersion measures ${\rm
DM_{IGM}}$ derived from FRBs (i.e., the combination $D_{L}\cdot{\rm
DM_{IGM}}$). Moreover, unlike the traditional standard-siren approach (i.e.,
the $D_{L}$ method) and the $\rm DM_{IGM}$ method that rely on the optimization
of the Hubble constant $H_0$, this $D_{L}\cdot{\rm DM_{IGM}}$ method has the
advantage of being independent of $H_0$. Through Monte Carlo simulations, we
prove that the $D_{L}\cdot{\rm DM_{IGM}}$ method is more effective to constrain
cosmological parameters than $D_{L}$ or ${\rm DM_{IGM}}$ separately, and
enables us to achieve accurate multimessenger cosmology from around 100 GW/FRB
systems. Additionally, even if GW/FRB associations are not exist, the
methodology developed here can still be applied to those GWs and FRBs that
occur at the same redshifts.
