Fuzzy neural networks with fuzzy weights and fuzzy biases

An architecture of multi-layer feedforward neural networks whose weights and biases are given as fuzzy numbers is proposed. The fuzzy neural network with the proposed architecture maps an input vector of real numbers to a fuzzy output. The input-output relation of each unit is defined by the extension principle. A learning algorithm of the fuzzy neural networks is derived for real input vectors and fuzzy target outputs. The derived learning algorithm is extended to the case of fuzzy input vectors and fuzzy target outputs