The task of the first learning phase is to build an initial partitioning of the input dimensions and to generate basic rules with these partitions to cover the input data points. The partitioning and the specification of the antecedents depend only on the input values of the data and not on their classes. Therefore they need not to be modified. However, the class information and thus the cost matrix must be used to determine the correct consequents.
The original NEFCLASS system uses the following evaluation measure which is based on the activations of rules and the correctness of their classification. Let denote the class of a pattern p in the learning dataset and the activation of rule unit r for pattern p. Then the accumulated activation of a rule r for a class c is the sum
is calculated for each rule r and each class c. The consequent of the rule is set to that class that results in the highest accumulated activation. This measure is a heuristic, where using the activation supports patterns lying closer to the centers of the fuzzy rules. We modified this to a heuristic estimation of the misclassification costs that would occur if the consequent was changed to a class c. The costs are calculated as
and the consequent of rule r is set to the class that minimizes this term.
The original NEFCLASS offers the possibility to reduce the number of initially found rules. The used algorithm is also available as a separate pruning step and thus is described in Sect. 2.3.