Comment on "combinatorial rule explosion eliminated by a fuzzy rule configuration"
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. In [1], the authors 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.
curse of dimensionality approximate reasoning fuzzy implication fuzzy sets