Dynamic Fuzzy Machine Learning

The intersection and union operations of the discretization scheme of set $\left({\stackrel{\leftharpoonup }{U}}_N,{\stackrel{\rightharpoonup }{U}}_N\right)$ are

$\begin{array}{l}\left({\overleftarrow{\pi }}_i,{\stackrel{\rightharpoonup }{\pi }}_i\right)\cap \left({\overleftarrow{\pi }}_j,{\stackrel{\rightharpoonup }{\pi }}_j\right)=\left\{\left({\pi }_1^i,{\pi }_1^i\right)\wedge \left({\pi }_1^i,{\pi }_1^j\right),\left({\pi }_2^i,{\pi }_2^j\right)\wedge \left({\pi }_2^j,{\pi }_2^j\right),\dots ,\left({\pi }_n^i,{\pi }_n^j\right)\wedge \left({\pi }_n^i,{\pi }_n^j\right)\right\}\\ \left({\overleftarrow{\pi }}_i,{\stackrel{\rightharpoonup }{\pi }}_i\right)\cup \left({\overleftarrow{\pi }}_j,{\stackrel{\rightharpoonup }{\pi }}_j\right)=\left\{\left({\pi }_1^i,{\pi }_1^i\right)\vee \left({\pi }_1^i,{\pi }_1^j\right),\left({\pi }_2^i,{\pi }_2^j\right)\vee \left({\pi }_2^j,{\pi }_2^j\right),\dots ,\left({\pi }_n^i,{\pi }_n^j\right)\vee \left({\pi }_n^i,{\pi }_n^j\right)\right\}\end{array}$

The division of $\left({\stackrel{\leftharpoonup }{\pi }}_i,{\stackrel{\rightharpoonup }{\pi }}_i\right)\cap \left({\stackrel{\leftharpoonup }{\pi }}_j,{\stackrel{\rightharpoonup }{\pi }}_j\right)$ to an instance set $\left({\stackrel{\leftharpoonup }{U}}_N,{\stackrel{\rightharpoonup }{U}}_N\right)$ is the biggest one that is smaller than $\left({\stackrel{\leftharpoonup }{\pi }}_i,{\stackrel{\rightharpoonup }{\pi }}_i\right),\left({\stackrel{\leftharpoonup }{\pi }}_j,{\stackrel{\rightharpoonup }{\pi }}_j\right).({\stackrel{\leftharpoonup }{\pi }}_i,$