We derive a back-propagation learning algorithm of fuzzy neural networks using fuzzy operations, which preserves the shapes of fuzzy numbers, in order to utilize fuzzy if-then rules as well as numerical data in the learning of neural networks for classification problems and for fuzzy control problems. By introducing the shape preseving fuzzy operation into a neural network, the proposed network simplifies fuzzy arithmetic operations of fuzzy numbers with exact result in learning the network. And we illustrate our approach by computer simulations on numerical examples.