A Framework of Using NURBS Curve as the Membership Functions in the Neural-Fuzzy System

Abstract

Abstract A novel neural-fuzzy system is developed by using the NURBS (Non-uniform Rational B-spline) curve as the membership functions in this paper. The neural-fuzzy system uses the fuzzy logic rule to estimate the output of the systems and uses the weight updating method in neural networks to adjust the rules. The NURBS interpolation method is proposed to construct adaptable membership functions for the proposed neural-fuzzy system. Since the shape of a NURBS curve is controlled by adjusting the control vertices and their weights, changing a control vertex and its weight will only affect the curve shape locally. This local control property reduces the number of iterations of learning in the system. Due to the adaptability of the NURBS membership function, the proposed system will need fewer fuzzy rules compared to existing systems but result in faster error convergence and better accuracy in system identification. The simulation results in Test Examples show that the presented NURBS neural-fuzzy system can identify complex systems with good accuracy and fast learning speed.