Avoidance of rule explosion by mapping fuzzy systems to a union rule configuration

We present a novel mapping whereby a classical fuzzy system, based on an intersection rule configuration (IRC), is converted to a union rule configuration (URC) system. Previous work has demonstrated that URC fuzzy systems avoid rule explosion, where a linear increase in the number of antecedents gives rise to an exponential increase in the number of fuzzy rules. However, there has been some doubt as to the validity of URC systems and previous findings. We resolve lingering questions and prove that any arbitrary IRC system can be converted to a URC system with identical performance. Further, we show that URC systems do avoid rule explosion for many problems. Finally, we note that a URC system is a universal approximator.