Using default rules in fuzzy control

A serious problem of fuzzy control is that the number of rules increases exponentially with the number of input variables. In this paper we investigate an extended Takagi-Sugeno-Kang fuzzy controller that is capable of dealing with ´default rules´. The basic motivation for such rules is an easy observation: In many applications there are critical regions of the input space, where dedicated rules should be applied. But, very often, there are noncritical regions as well. In these regions slight deviations of the output value do no harm. Consequently, we should focus our attention upon the critical regions whereas for the noncritical regions a rough approximation seems adequate. Default rules support this approach since they allow the formalization of statements like ´approximate function f(x) by √x unless x is in a region where we have a better approximation´. Eventually, this permits smaller rule bases