A goodness-function for trained fuzzy neural networks

Fuzzy neural networks are fully fuzzified neural networks. These networks can be trained with crisp and fuzzy data. In (Feuring, 1995, and Feuring and Lippe, 1995) it was shown that fuzzy neural networks can approximate arbitrary fuzzy continuous functions based on the extension principle. These functions have some further properties which are pointed out in this paper. These properties lead to a criterion for choosing a training set and yield a definition of the goodness of a trained fuzzy neural network. By defuzzifying the fuzzy network the authors get a crisp neural net. The goodness of the fuzzy net leads to the description of the maximum error of the crisp network for arbitrary crisp input data