Dynamic Fuzzy Machine Learning

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 ...