Direct implementation of fuzzy control with basis function networks

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