Rules represent dependencies in the dataset, and represent extracted knowledge which can be used when classifying new objects not in the original information system. When the reducts were found, the job of creating definite rules for the value of the decision attribute of the information system was practically done. To transform a reduct (relative or not) into a rule, one only has to bind the condition attribute values of the object class from which the reduct originated to the corresponding attributes of the reduct. Then, to complete the rule, a decision part comprising the resulting part of the rule is added. This is done in the same way as for the condition attributes. The rules in our example are as follows.
¯
The ``rules'' derived with basis in does not specify the resulting attribute value for income, since it is not the same for all the objects in the class. It may therefore be called it a vague category. A better way of of presenting this than through a question mark would be to say e.g. that if education is poor, then there is a 50% chance that income is low, and that there is a 50 % chance that income is medium.
If a new object is introduced to the example data set with the decision
value missing, one could attempt to determine this value by using the
previously generated rules. If exactly one rule which fits is found, the
classification is straightforward. This also implies that the object is
in the lower approximation of the class to which it is classified to
belong to. For objects contained in the boundary region of different
classes, no such consistent decision can be made. More on decision
making in the chapter about classification, Chapter 
.