CONSTRAINED DEFUZZIFICATION

We look at the problem of defuzzification in situations in which in addition to the usual fuzzy output of the controller there exists some ancillary restriction on the allowable defuzzified values. We provide two basic approaches to address this problem. In the first approach we enforce the restriction by selecting the defuzzified value through a random experiment in which the values which have nonzero probabilities are in the allowable region, this method is based on the RAGE defuzzification procedure and makes use of a nonmonotonic conjunction operator. The second approach which in the spirit of the commonly used methods, a kind of expected value, converts the problem to a constraint optimization problem.