学習機能を持つファジィクラシファイアの入力不変性

抄録

In our previous work we have developed fuzzy classifiers with ellipsoidal regions and with hyperbox regions. In this paper we discuss linear transformation invariance of these classifiers. First, we prove that the fuzzy classifier with ellipsoidal regions, which is based on the Mahalanobis distance, has invariance for linear transformation of input variables. Then we prove that the fuzzy classifier with hyperbox regions, whose surfaces are parallel to input axes, has limited scale invariance. Finally, we show the advantages of our classifiers over neural networks by the performance evaluation of benchmark data.