In order to construct fuzzy systems automatically, there are many studies on combining fuzzy inference with neural networks. In these studies, fuzzy models using self-organization and vector quantization have been proposed. It is well known that these models construct fuzzy inference rules effectively representing distribution of input data, and not affected by increment of input dimensions. In this paper, we propose a destructive fuzzy modeling using neural gas network and demonstrate the validity of a proposed method by performing some numerical examples.

In this paper we suggest the "goodness" of models using the imformation criterion AIC. The information criterion AIC is a statistic to estimate the badness of models. When we usually make the fuzzy rules, we aim to minimize inference error and the number of rules. But these conditions are the criteria to acquire an optimum rule-model by using the training data. In the general case of fuzzy reasoning, we aim to minimize the inference error for not only given training data, but also unknown data. So we have introduced a new information criterion based on AIC into the appraised criterion for estimating the acquired fuzzy rules. Experimental results are given to show the validity of using AIC.

In order to provide a fuzzy system with learning function, numerous studies are being carried out to combine fuzzy systems and neural networks. The self-tuning methods using the descent method have been proposed. The constructive and the destructive methods are more powerful than other methods using neural networks (or descent method). On the other hand the destructive method is superior in the number of rules and inference error and inferior in learning speed to the constructive method. In this paper, we propose a new learning method combining the constructive and the destructive methods. The method is superior in the number of rules, inference error and learning speed to the destructive method. However, it is inferior in learning speed to the constructive method. Therefore, in order to improve learning speed of the proposed method, simplified learning methods are proposed. Some numerical examples are given to show the validity of the proposed methods.