  Cosmological models and their corresponding parameters are widely debated
because of the current discrepancy between the results of the Hubble constant,
$H_{0}$, obtained by SNe Ia, and the Planck data from the Cosmic Microwave
Background Radiation. Thus, considering high redshift probes like Gamma-Ray
Bursts (GRBs) is a necessary step. However, using GRB correlations between
their physical features to infer cosmological parameters is difficult because
GRB luminosities span several orders of magnitude. In our work, we use a
3-dimensional relation between the peak prompt luminosity, the rest-frame time
at the end of the X-ray plateau, and its corresponding luminosity in X-rays:
the so-called 3D Dainotti fundamental plane relation. We correct this relation
by considering the selection and evolutionary effects with a reliable
statistical method, obtaining a lower central value for the intrinsic scatter,
$\sigma_{int}=0.18 \pm 0.07$ (47.1 \%) compared to previous results, when we
adopt a particular set of GRBs with well-defined morphological features, called
the platinum sample. We have used the GRB fundamental plane relation alone with
both Gaussian and uniform priors on cosmological parameters and in combination
with SNe Ia and BAO measurements to infer cosmological parameters like $H_{0}$,
the matter density in the universe ($\Omega_{M}$), and the dark energy
parameter $w$ for a $w$CDM model. Our results are consistent with the
parameters given by the $\Lambda$CDM model but with the advantage of using
cosmological probes detected up to $z=5$, much larger than the one observed for
the furthest SNe Ia.
