where ${\text{pro}}_{k}=\left|\text{Par}\begin{array}{c}\left({\overleftarrow{v}}_{k},{\overrightarrow{v}}_{k}\right)\\ \left({\overleftarrow{A}}_{D},{\overrightarrow{A}}_{D}\right)\end{array}\left(\overleftarrow{U},\overrightarrow{U}\right)\right|/\left|\left(\overleftarrow{U},\overrightarrow{U}\right)\right|$ denotes the ratio of the number of instances belonging to class $\left({\overleftarrow{v}}_{k},{\overrightarrow{v}}_{k}\right)$ in instance set $\left(\overleftarrow{U},\overrightarrow{U}\right)$ to the total set of instances.

We set ${T}_{\left({\overleftarrow{A}}_{i},{\overrightarrow{A}}_{i}\right)}\left(\overleftarrow{U},\overrightarrow{U}\right)=1-{\text{Cer}}_{\left({\overleftarrow{A}}_{i},{\overrightarrow{A}}_{i}\right)}\left(\overleftarrow{U},\overrightarrow{U}\right)=1-{\displaystyle {\sum}_{k=1}^{n}{\text{pro}}_{k}{\text{Cer}}_{\left({\overleftarrow{A}}_{i},{\overrightarrow{A}}_{i}\right)}^{k}\left(\overleftarrow{U},\overrightarrow{U}\right)}$ as the attribute selection criteria in the decision tree classification. The range of ${T}_{\left({\overleftarrow{A}}_{i},{\overrightarrow{A}}_{i}\right)}\left(\overleftarrow{U},\overrightarrow{U}\right)$

If ${T}_{\left({\overleftarrow{A}}_{i},{\overrightarrow{A}}_{i}\right)}\left(\overleftarrow{U},\overrightarrow{U}\right)=0,$ the conditional attribute $\left({\overleftarrow{A}}_{i},{\overrightarrow{A}}_{i}\right)$ has a ...

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