Robust Function Approximation Using Ellipsoidal Fuzzy Rules

概要

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This paper discusses robust function approximation when the Takagi-Sugeno type model is used for the consequent part of fuzzy rules. With this model, the parameters of the linear equation that defines the output value of the fuzzy rule are determined by the least-squares method. Therefore, if the training data include outliers, the method fails to determine the parameter values correctly. To overcome this problem we use the least-median-of-squares method. Among the original training data set, we randomly select training data more than the number of parameters, and determine the parameter values using the least-squares method. We repeat this many times and determine the parameters with the smallest median of squared errors. We compare the proposed method with the least-squares method and the conventional least-median-of-squares method using the data generated by the Mackey-Glass differential equation.