Fuzzy rules are a popular basis for classifiers due to their rather intuitive and understandable application. The use of linguistic variables eases the readability and interpretability of the rule base. Automatic induction of fuzzy rules from data is therefore an interesting topic. A common approach to automatic rule generation is based on neuro-fuzzy systems [1, 6, 12].
In many practical domains the available training data is more or less unbalanced, i.e. the number of cases of each class varies. This causes problems for many classification systems and their associated learning algorithms. This is especially obvious if the classes are not well separated. In such cases classifiers tend to predict the majority class. This may be completely reasonable to minimize the error measure. However, the classifiers do not take into account the semantics of the classes. Some classes may be more related to each other than others, and thus misclassifications between them may be less severe. Classes may not behave symmetrically, i.e. falsely classifying class A as B is more expensive than falsely classifying class B as A. In many domains it is desirable or even necessary to let the user model these asymmetries.
A straightforward way to model them would be to directly specify the costs of each possible misclassification. This is the basic idea of our approach, which we have incorporated into the learning system. For the implementation of the presented approaches we modified the NEFCLASS (NEuro Fuzzy CLASSification) model [7, 8], a neuro-fuzzy model for data analysis. It was designed as an interactive classification tool, that allows the user to influence the automatic learning and classification process.
We applied the modified NEFCLASS to a machine vision problem where the severeness of misclassifications is asymmetric. In our classification task too many false negatives can completely prevent the correct recognition of objects, whereas false positives lead `only' to considerably longer execution times. The next sections give more detailed descriptions of the vision task and the original NEFCLASS system. The modifications of the latter are described in Sect. 2. Its application to the vision task and the results are described and commented in Sect. 3 and 4.
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