  The principle of maximum conformality (PMC) has been suggested to eliminate
the renormalization scheme and renormalization scale uncertainties, which are
unavoidable for the conventional scale setting and are usually important errors
for theoretical estimations. In this paper, by applying PMC scale setting, we
analyze two important inclusive Standard Model Higgs decay channels,
$H\rightarrow b\bar{b}$ and $H\rightarrow gg$, up to four-loop and three-loop
levels accordingly. After PMC scale setting, it is found that the conventional
scale uncertainty for these two channels can be eliminated to a high degree.
There is small residual initial scale dependence for the Higgs decay widths due
to unknown higher-order $\{\beta_i\}$-terms. Up to four-loop level, we obtain
$\Gamma(H\rightarrow b\bar{b}) = 2.389\pm0.073 \pm0.041$ MeV and up to
three-loop level, we obtain $\Gamma(H\rightarrow gg) = 0.373\pm0.030$ MeV,
where the first error is caused by varying $M_H=126\pm4$ GeV and the second
error for $H\to b\bar{b}$ is caused by varying the $\overline{\rm MS}$-running
mass $m_b(m_b)=4.18\pm0.03$ GeV. Taking $H\to b\bar{b}$ as an example, we
present a comparison of three BLM-based scale setting approaches, e.g. the
PMC-I approach based on the PMC-BLM correspondence, the $R_\delta$-scheme and
the seBLM approach, all of which are designed to provide effective ways to
identify non-conformal $\{\beta_i\}$-series at each perturbative order. At
four-loop level, all those approaches lead to good pQCD convergence, they have
almost the same pQCD series, and their predictions are almost independent on
the initial renormalization scale. In this sense, those approaches are
equivalent to each other.
