On the use of Fourier methods in URC fuzzy system design

Previously (J.J. Weinschenk et al., 2003), we demonstrated that rule explosion is avoidable in fuzzy inference engines by mapping an intersection rule configuration (IRC) to a union rule configuration (URC). Although a conversion between IRC and URC systems is simple for a special, additively separable class of IRC rule tables, the conversion process is more difficult when the IRC rule table is additively inseparable. In a previous paper, we demonstrated that a layered URC architecture can implement these types of systems, but did not provide a method for computing the weights. In this follow-on paper, we provide a Fourier-based algorithm for computation of the weights. We also prove that this technique is optimal in the sense that the mean-square approximation error is minimized for a fixed amount of resources. Finally, through the course of an example, we explore the implementation issues and evaluate the overall effectiveness of the technique.