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The presentation is focused on comparison of neural networks and fuzzy systems. Advantages and disadvantages of both technologies are discussed. Fuzzy systems are relatively easy to design but number of inputs in the system are significantly limited. It is very difficult to design neural networks so rather they have to be trained instead. Neural networks produce much smoother nonlinear mapping than fuzzy systems. When neural networks are selected then researchers are facing two dilemmas: what should be neural network architectures and how to train them. The presentation gives answers for both problems. It was found that Bridged Multilayer Preceptron BMLP are a much better architecture than popular MLP architecture. It is faster to train and more complex problems can be solved with fewer neurons. Training of neural networks is not easy. For example most of the existing software cannot train close to optimal neural network so networks with excessive number of neurons are being used by most researchers. Such networks indeed can be trained to very small errors using training patterns but they are not able to respond correctly for new patterns not used in training. A new NBN learning algorithm is presented in this work. This algorithm is not only up to 1000 times faster than the popular EBP algorithm, but it can train all neural network architectures. More importantly it can train close to optimum neural networks which were not able to be trained before.