Direct implementation of fuzzy control with basis function networks
Kenneth James Hunt, R. Haas, Roderick Murray‐Smith · 2002
There is significant interest in the interplay between fuzzy systems and neural networks. Jang and Sun (1993) established the functional equivalence of Gaussian radial basis function (RBF) networks and a restricted class of Takagi-Sugeno-type (1985) fuzzy systems. This result was extended to the full TS-model by Hunt et al. (1994) who employed networks with local models and ellipsoidal basis functions. The restriction to Gaussian type basis functions, and therefore to Gaussian-shaped fuzzy membership functions, was later removed by Hunt et al. through employment of spline-based networks. This covers fuzzy systems with a broad range of membership function shapes (triangular and trapezoidal shapes are common special cases). In this paper we present a generalised form of the functional equivalence theorem and discuss its relevance for the direct implementation of fuzzy control systems in the form of neural networks.>