  The generalized uncertainty principles (GUP) and modified dispersion
relations (MDR) are much like two faces for one coin in research for the
phenomenology of quantum gravity which apparently plays an important role in
estimating the possible modifications of the black hole thermodynamics and the
Friedmann equations. We first reproduce the horizon area for different types of
black holes and investigate the quantum corrections to Bekenstein-Hawking
entropy (entropy-area law). Based on this, we study further thermodynamical
quantities and accordingly the modified Friedmann equation in four-dimensional
de Sitter-Schwarzschild, Reissner-N\"{o}rdstrom and
Garfinkle-Horowitz-Strominger black holes. In doing this we applied various
quantum gravity approaches. The MDR parameter relative to the GUP one is
computed and the properties of the black holes are predicted. This should play
an important role in estimating response of quantum gravity to the various
metric-types of black holes. We found a considerable change in the
thermodynamics quantities. We find that the modified entropy of
de-Sitter-Schwarzshild and Reissner-N\"{o}rdstrom black holes starts to exist
at a finite standard entropy. The Garfinkle-Horowitz-Strominger black hole
shows a different entropic property. The modified specific heat due to GUP and
MDR approaches vanishes at large standard specific heat, while the corrections
due to GUP result in different behaviors. The specific heat of modified
de-Sitter-Schwarzshild and Reissner-N\"{o}rdstrom black holes seems to
increase, especially at large standard specific heat. In the early case, the
black hole cannot exchange heat with the surrounding space. Accordingly, we
would predict black hole remnants which may be considered as candidates for
dark matter.
