Comments on "Combinatorial rule explosion eliminated by a fuzzy rule configuration" [with reply]

In the original paper (IEEE Trans. Fuzzy Syst., vol.6, p.1-11, 1998), Combs and Andrews proved the following logical equivalence (stated here for two antecedents p and q and one consequent r, but easily generalize to an arbitrary number of antecedents and consequents): [(p/spl and/q)/spl rArr/r]/spl hArr/[(p/spl rArr/r)V(q/spl rArr/r)]. This is a very significant result because it suggests that we can replace multi-antecedent rules with an interconnection of single antecedent rules, which eliminates the rule explosion that is associated with multi-antecedent rules. Combs and Andrews refer to the left-hand side of this equivalence as an intersection rule configuration (IRC) and to its right-hand side as a union rule configuration (URC). Their result gives rise to two distinctly different paths for the design of fuzzy logic systems; IRC, which leads to rule explosion, and URC, which does not. The authors discuss four points about the IRC/spl hArr/URC relation. The original authors reply, acknowledging some of the points and stating that they would present their results differently if starting now.