Function approximation using non-normalized SISO fuzzy systems Original Research Article

In this paper we propose an improvement in the field of fuzzy function approximation. It is well known that tuning the shape and the position of the membership functions, improves the approximation, but what about changing the heights of these functions? Usually the system is normalized so that the heights of the membership functions are set to 1, but an interesting result can be obtained if we make them variable, giving a further degree of freedom to the fuzzy system. We will use this feature in order to achieve a better function approximation, to build a second-order derivative approximation or to make the derivative of our approximation continuous. We will show also how to increase the spectral purity of the approximation function as in the case of sinusoidal functions. This approach will be analyzed under a theoretical point of view, comparing the results with those obtained with the classical approach.