This paper examines the ability of fuzzy neural networks to the approximate realization of fuzzy if-then rules. Fuzzy neural networks in this paper are characterized by fuzzy weights and fuzzy biases. This means that the weights and biases are given b...
This paper examines the ability of fuzzy neural networks to the approximate realization of fuzzy if-then rules. Fuzzy neural networks in this paper are characterized by fuzzy weights and fuzzy biases. This means that the weights and biases are given by fuzzy numbers instead of real numbers. First, the input-output relation of a three-layer feedforward fuzzy neural network is defined for fuzzy input vectors by the extension principle of Zadeh. Next, a cost function is defined for the level sets of fuzzy actual outputs and fuzzy target outputs. A learning algorithm is derived from the cost function in a similar manner as the back-propagation algorithm. Last, using a numerical example, the fuzzy neural networks with fuzzy weights and fuzzy biases are compared with other fuzzy neural networks with crisp weights and crisp biases designed for handling fuzzy input-output data.