Learning of fuzzy connection weights in fuzzified neural networks

We examine how fuzzy connection weights are adjusted in fuzzified neural networks by various computer simulations. Our fuzzified neural networks are three-layer feedforward neural networks where connection weights are given as fuzzy numbers. The fuzzified neural networks can handle fuzzy numbers as inputs and targets. First, we examine how the fuzziness in training data propagates to the fuzziness of the connection weights by the learning of the fuzzified neural networks. Next, we examine the ability of the fuzzified neural networks to approximately realize fuzzy if-then rules. In computer simulations, we compare three types of connection weights: real numbers, symmetric triangular fuzzy numbers and non-symmetric trapezoidal fuzzy numbers. By computer simulations, it is demonstrated that the non-fuzzy neural networks with the real number connection weights do not work well for some test problems where the fuzziness of targets is much larger than the fuzziness of inputs. On the contrary, when the fuzziness of targets is much smaller than the fuzziness of inputs, the fuzzy connection weights are not necessary