Fuzzy regression analysis by fuzzy neural networks and its application

In this paper, we propose a fuzzy regression method using fuzzy neural networks when a membership value is attached to each input-output pair. In our method, the membership value represents the degree of importance of the corresponding input-output pair. First, we show the architecture of fuzzy neural networks that have fuzzy weights and fuzzy biases. Next, we define a cost function that is based on the inclusion relation between the fuzzy output of the fuzzy neural network and the corresponding crisp target with a membership value. A learning algorithm is derived from the cost function. The learning algorithm derived trains the fuzzy neural network so that the crisp target is included in the level set of the actual fuzzy output. The level set is defined by the membership value of the crisp target. Finally, we demonstrate the ability of the proposed method using a quality evaluation problem of injection moldings