# Optimal Classification/Rypka Method/Equations/Separatory/Characteristic/Empirical/Separation

## Separation Stages

### Initial separation

${\displaystyle S_{j}={\frac {\left[(G^{2})-\sum _{l=0}^{R}n_{l}^{2}\right]}{2}}}$, where:[1]

• Sj is the initial empirical separatory value for each characteristic, where,
j = 0...C and is the index of the jth characteristic in the group and C is the number of characteristics in the group, and,
l = 0...R and is the truth table value of the jth characteristic, where R is the truth table size, where:
R = V0, and,
• V is the highest value of logic in the group and,
• 0 is the target set exponent for a single characteristic, and,
• G is the number of elements in the bounded class.

### Subsequent separation

${\displaystyle S={\frac {\left[(G^{2})-\sum _{l=0}^{R}n_{l}^{2}\right]}{2}}}$, where:

• Sj is the initial empirical separatory value for each characteristic, where,
l = 0...R and is the target set truth table index value, where R is the target set truth table size value, where:
R = VK, and,
• V is the highest value of logic in the group and,
• K is the number of characteristics in the target set, and,
• G is the number of elements in the bounded class.

## Notes

1. Must be applied initially to each characteristic. (The equations have been implemented in Mathcad and using the Visual Basic programming language. See Application_Example