  We propose a new cosmological model that considers dark matter as a
barotropic fluid with a constant equation of state parameter and interprets
dark energy as the phenomenological emergent dark energy rather than a
cosmological constant. This proposal is based on extensive research on the
extended properties of dark matter in the context of a cosmological constant
and the intriguing findings that have emerged from our exploration of dark
matter properties within the context of PEDE in our previous studies. We then
place constraints on this model in light of the Planck 2018 Cosmic Microwave
Background (CMB) anisotropies, baryon acoustic oscillation (BAO) measurements,
the Pantheon compilation of Type Ia supernovae, a prior on $H_0$ that based on
the latest local measurement by Riess et al., and the combination of KiDS and
the VISTA Kilo-Degree Infrared Galaxy Survey (KiDS+VIKING-450). The results
indicate a preference for a positive dark matter equation of state parameter at
68\% confidence level for CMB+BAO, CMB+BAO+Pantheon and CMB+BAO+Pantheon+$H_0$
datasets. Furthermore, the Hubble tension between all of the datasets we used
with R22 is very close to those of the PEDE, and the $S_8$ tension between
Planck 2018 and KiDS+VIKING-450 is reduced from 2.3$\sigma$ in the PEDE model
to 0.4$\sigma$ in the new model. However, Bayesian evidence indicates that PEDE
favors our new model with very strong evidence from all the datasets considered
in this study. Consequently, we conclude that the PEDE+$w_{\rm dm}$ model is
not a viable alternative to the PEDE model.
