Fuzzy rules extraction directly from numerical data for function approximation

In our previous work (1993) we developed a method for extracting fuzzy rules directly from numerical input-output data for pattern classification. In this paper we extend the method to function approximation. For function approximation, first, the universe of discourse of an output variable is divided into multiple intervals, and each interval is treated as a class. Then the same as for pattern classification, using the input data for each interval, fuzzy rules are recursively defined by activation hyperboxes which show the existence region of the data for the interval and inhibition hyperboxes which inhibit the existence region of data for that interval. The approximation accuracy of the fuzzy system derived by this method is empirically studied using an operation learning application of a water purification plant. Additionally, we compare the approximation performance of the fuzzy system with the function approximation approach based on neural networks