Dynamic Fuzzy Machine Learning

The operator “ ≤ ” defines a partial order relation on the partition of domain U(the relation ≤ is reflexive, anti-symmetric, and transitive). If π1 ≤ π2, then we say partition π1 is smaller than π2.

Take the partition as a computing object, and define intersection and union operations:

π1 ∧ π2 denotes the largest partition smaller than both π1 and π2;

π1 ∨ π2 denotes the smallest partition larger than both π1 and π2.

The union operation of partitions is equivalent to the supremum in computing, and the intersection operation is equivalent to the infimum operation. At the same time, the thickness of the partition can be defined so that we have a partition lattice. The partition lattice is introduced into the DFDT because the process of constructing ...