Function approximation using non-normalized SISO fuzzy systems

In this paper we propose an improvement in the field of fuzzy function appr oximation. It is well known that tuning the shape and the position of the m embership functions, improves the approximation, but what about changing th e 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 freed om to the fuzzy system. We will use this feature in order to achieve a bett er function approximation, to build a second-order derivative approximation or to make the derivative of our approximation continuous. We will show al so how to increase the spectral purity of the approximation function as in the case of sinusoidal functions. This approach will be analyzed under a th eoretical point of view, comparing the results with those obtained with the classical approach. (C) 2001 Elsevier Science Inc. All rights reserved.