Multiobjective fuzzy genetics-based machine learning with a reject option

Yusuke Nojima, Hisao Ishibuchi

Abstract: Classifier design for a classification problem with M classes can be viewed as finding an optimal partition of its pattern space into M disjoint subspaces. However, this is not always a good strategy especially when training patterns from different classes are heavily overlapping in the pattern space. A simple but practically useful idea is the use of a reject option. In this case, the pattern space is partitioned into (M+1) disjoint subspace where the classification of new patterns is rejected in the (M+1)th subspace. In this paper, we discuss the design of fuzzy rule-based classifiers with a reject option. The rejection subspace is specified by a threshold value for the difference of a kind of matching degrees between the best matching class and the second best matching class. The important research question is how to specify the threshold value. We examine the following two approaches: One is manual specification after designing a fuzzy rule-based classifier, and the other is simultaneous multiobjective optimization of a threshold value and a fuzzy rule-based classifier. In the latter approach, we use three objectives: maximization of the correct classification, and minimization of the rejection and the complexity of the classifier.