Rule-based fuzzy systems with weighted power mean firing operator as universal approximators

Certain classes of fuzzy rule-based systems have been shown to be universal approximators, capable of approximating any continuous mapping on a compact subset of the domain. In previous cases, this property has been proven for fuzzy systems employing t-norms to determine the firing level of each rule. In this paper, we prove that use of the weighted power mean to determine rule firing levels also results in a universal approximator. While it is only a t-norm in certain special cases, the weighted power mean is a more general aggregation operator, capable of providing greater logical flexibility in a rule. This will be of particular interest in computing with words (CWW) applications, where such flexibility is needed the better to mimic human reasoning.