Fuzzy neural networks are overlapping

Fuzzy neural networks can be trained with crisp and fuzzy data. J. Buckley and Y. Hayashi (1994) have shown that these networks are monotonic when extension principle based operations are used to compute the network output. This means that the fuzziness of the network output increases or decreases whenever the fuzziness of the input increases or decreases respectively. In this paper we show that these networks are also overlapping. This property provides us with a means to theoretically analyse the output behaviour of fuzzy neural networks. We briefly present a learning algorithm. Finally we find our theoretical observations confirmed testing the trained network