$T$	the total number of decision trees in the random forest
$\mathcal{Y}$	a collection of all target labels $y$
$t$	decision tree $t$
$x$	single sample
$y$	the predicted label of $x$ in the random forest, $y\in \mathcal{Y}$
$r_k^t\left(y\right)$	the ratio of samples belonging to label $y$ on node $k$ in decision tree $t$
$L{I}_k^t\left(y\right)$	the local importance of node $k$ in decision tree $t$ with predicted label $y$
$f_t\left(x\right)$	the prediction of sample $x$ in decision tree $t$
$v_t\left(x,y\right)$	the binary voting variable of decision tree $t$ on whether the sample prediction equals to $y$
$P_t\left(x,y\right)$	the possibility that the sample prediction equals to $y$ in decision tree $t$
$R{S}_k\left(x,y\right)$	the reliability score calculated by the decision path sample $x$ passes in decision tree $t$
$R{S}_{min}\left(x,y\right)$, $R{S}_{max}\left(x,y\right)$	the minimum and maximum values of RS in all decision trees
$H_{RF,hard}$, $H_{RF,soft}$, $H_{DPRF,hard}$, $H_{DPRF,soft}$	the voting results of $RF$ and $DPRF$ under the hard and soft voting rule, respectively
$𝒟𝒫(t,x)$,$𝒟{𝒫}_{\mathrm{miss}}(t,x)$	the collection of all the nodes of the decision path in decision tree $t$, and the collection of all the corresponding missing nodes, respectively.