  We consider the propagation of gravitational waves in the late-time Universe
in the presence of matter distribution inhomogeneities, and we also consider
the cosmic fluid to be viscous. In this work, we investigate the cumulative
effect of inhomogeneities and viscosity of the cosmic-fluid on the observables
associated with the sources of the gravitational waves. Employing Buchert's
averaging procedure in the backreaction framework, we consider a model of
spacetime in which matter is distributed in-homogeneously across space. Using
the modified redshift versus distance relation, through the averaging process
in the context of the model, we study the variation of the redshift-dependent
part of the observed gravitational wave amplitude for different combinations of
our model parameters while simultaneously considering damping of the
gravitational wave amplitude due to viscosity of the cosmic-fluid. Then, we
investigate the differences occurring in the variation of the
redshift-dependent part of the observed gravitational wave amplitude due to
consideration of viscous attenuation. We show that there are significant
deviations after the inclusion of viscous attenuation in our analysis,
depending on the chosen value of the coefficient of viscosity. Our result
signifies the importance of the effect of viscosity, within the model of an
inhomogeneous Universe, on precision measurements of parameters of
compact-binary sources of gravitational waves.
