Soft Computing and Its Applications, Volume One

586 Soft Computing and Its Applications

Example 5.19 The C-lower approximation of (M, poor) is the formula:

The C-boundary of is the formula:

After simplication we get the following approximations:

,

.

The concepts of the lower and upper approximation of a decision allow us to dene

the following decision rules:

,

,

.

For instance, from the approximations given in the example above, we get the fol-

lowing decision rules:

From these denitions it follows that any decision can be uniquely described by

the following two decision rules:

Rough Set 587

,

.

From the above calculations we can get two decision rules: