  Since gravitational waves (GWs) propagate freely through a perfect fluid,
coalescing compact binary systems as standard sirens allow to measure the
luminosity distance directly and provide distance measurements unaffected by
the cosmic opacity. DECi-hertz Interferometer Gravitational-wave Observatory
(DECIGO) is a future Japanese space gravitational-wave antenna sensitive to
frequency range between target frequencies of LISA and ground-based detectors.
Combining the predicted future GW observations from DECIGO and three current
popular astrophysical probes (HII regions, SNe Ia Pantheon sample, quasar
sample) in electromagnetic (EM) domains, one would be able to probe the opacity
of the Universe at different redshifts. In this paper, we show that the cosmic
opacity parameter can be constrained to a high precision ($\Delta \epsilon\sim
10^{-2}$) out to high redshifts ($z\sim$5). In order to reconstruct the
evolution of cosmic opacity without assuming any particular functional form of
it, the cosmic opacity tests should be applied to individual redshift bins
independently. Therefore, we also calculate the optical depth at individual
redshifts and averaged $\tau(z)$ within redshift bins. Our findings indicate
that, compared with the results obtained from the HII galaxies and Pantheon SNe
Ia, there is an improvement in precision when the quasar sample is considered.
While non-zero optical depth is statistically significant only for redshift
ranges $0<z<0.5$, $1<z<2$, and $2.5<z<3.5$, such tendency is different from
that obtained in the framework of its parametrized form. Therefore the
importance of cosmic-opacity test without a prescribed phenomenological
function should be emphasized.
