Naturally De ned Membership Functions for Fuzzy Logic Systems and A Comparison with Conventional Set Functions

Abstract We point out that B spline basis functions are naturally de ned membership functions for fuzzy logic systems i e the speci cation of these functions depends only on the partition points of each linguistic variables no more necessarily also on the additional parameters if normal set functions are used Based on B spline basis functions a fuzzy controller can be constructed which works like an adaptive B spline interpolator Through comparative examples for function approximation we show that learning of such a fuzzy controller generally converges faster The approximation errors are in most cases not larger than the results achieved by using the normal set functions in some cases even smaller depending on the type of test functions The good approximation ability and the fast convergence of learning make this model suitable to supervised and unsupervised learning for a wide range of modelling and control tasks