  In cosmology, phenomenologically motivated expressions for running vacuum are
commonly parametrized as linear functions $\Lambda(H^2)$ or $\Lambda(R)$. Such
kind of models assume an equation of state for vacuum given by $\,\overline
P_\Lambda=-\,\overline\rho_\Lambda$, relating their background pressure
$\,\overline P_\Lambda$ and mean energy density
$\,\overline\rho_\Lambda\equiv\Lambda/8\pi G$. This equation of state requires
that the dynamic for vacuum is due to the energy exchange with the material
species. Most of the approaches to background level consider only the energy
exchange between vacuum and the transient dominant material component of the
universe. We extend such models assuming the running vacuum as the sum of
independent contributions $\,\overline\rho_{\Lambda}
=\sum_i\,\overline\rho_{\Lambda i}$, associated with (and interacting with)
each of the $i$ material species. We derive the linear scalar perturbations for
two running scenarios, modeling its cosmic evolution and identifying their
different imprints on the cosmic microwave background anisotropies and the
matter power spectrum. In the $\Lambda(H^2)$ scenario the running vacuum are
coupled with all the material species in the universe, whereas the $\Lambda(R)$
description only leads to coupling between vacuum and the non-relativistic
matter components; which produces different imprints of the two models on the
matter power spectrum. A comparison with the Planck 2015 data was made in order
to constrain the free parameters of the models. In the case of the
$\Lambda(H^2)$ model, it was found that $\Omega_\Lambda=0.705\pm0.027$ and
$H_0=69.6\pm2.9\, km\, Mpc^{-1}\, s^{-1}$, which diminish the tension with the
low redshift expectations.
