On the use of Fourier methods in URC fuzzy system design
Jeffrey J. Weinschenk, Robert J. Marks, W.E. Combs · 2005
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.