Comment on "Combinatorial rule explosion eliminated by a fuzzy rule configuration" [with reply]
Scott Dick, A. Kandel, W.E. Combs · IEEE Transactions on Fuzzy Systems · 1999
The "curse of dimensionality" is one of the key problems facing fuzzy systems theory today. Fuzzy systems are based on a set of IF-THEN rules and the structure of these fuzzy rules causes an exponential growth in the number of rules when more inputs are added, resulting in unwieldy rulebases. Many strategies have been proposed to alleviate the curse of dimensionality. Combs and Andrews (ibid., vol.6, p.1-11, 1998) attempt to reduce the growth of the fuzzy rulebase by proposing a disjunctive form for fuzzy rules. In the current paper, we comment on this approach and show that it is mathematically invalid, as illustrated by an example. Combs replies that the authors are addressing 2 different issues; whether the union and intersection rules of configuration be equivalent in fuzzy logic, and whether the latter can overcome the curse of dimensionality.