Fuzzy B-spline membership function (BMF) and its applications in fuzzy-neural control

Abstract

A general methodology for constructing fuzzy membership functions via B-spline curves is proposed. By using the method of least-squares, the authors translate the empirical data into the form of the control points of B-spline curves to construct fuzzy membership functions. This unified form of fuzzy membership functions is called a B-spline membership function (BMF). By using the local control property of a B-spline curve, the BMFs can be tuned locally during the learning process. For the control of a model car through fuzzy-neural networks, it is shown that the local tuning of BMFs can indeed reduce the number of iterations tremendously. This fuzzy-neural control of a model car is presented to illustrate the performance and applicability of the proposed method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>