Fuzzy function approximators with ellipsoidal regions

This paper discusses two types of fuzzy function approximators that dynamically generate fuzzy rules with ellipsoidal regions: a function approximator based on Takagi-Sugeno type model with the center of gravity defuzzification and a function approximator based on a radial basis function network. Hereafter the former is called FACG and the latter is called FALC. In FACG, for each training datum the number of the training data that are within the specified distance is calculated and the training datum which has the maximum number of the training data is selected as the center of a fuzzy rule and the covariance matrix is calculated using the training data around the center. Then the parameters of the linear equation that defines the output value of the fuzzy rule are determined by the least-squares method using the training data around the center. In FALC, the training datum with the maximum approximation error is selected as the center of a fuzzy rule, Then using the training data around the center, the covariance matrix is calculated, and the parameters of a linear equation that determines the output value are calculated by the least squares method. Performance of FACG and FALC is compared with that of multilayered neural networks and other fuzzy function approximators for the data generated by the Mackey-Glass differential equation and the data from a water purification plant.