The next definition introduces the concept of an indiscernibility relation. If such a relation exists between two objects, it means that all their attribute values are identical with respect to the attributes under consideration, and thus cannot be discerned (distinguished) between by regards of the considered attributes.
For the decision system given earlier, a calculation of gives the following result:
= {\1, 2}, {3}, {4, 5}\
One can see that the objects are grouped together, and that the groups
consist of objects that cannot be discerned between when using the selected
set of attributes. With a (equivalence) class is meant such a group.
The classes in tabular form is shown in Table
.
Class comes from
objects 1 and 2, class object 3, while class comes from
objects 4 and 5. Note that has two objects with different decision
attribute values.
| studies | education | works | |
| no | good | yes | |
| yes | good | yes | |
| no | poor | no |