Identifying Fuzzy Controllers Parameters

In fuzzy control, there is a large amount of parameters involved in the system design. Due to their interdependency, these parameters are sometimes conflicting causing an unavoidable trade-off among performance indices. It is difficult to discern the best combination of fuzzy parameters with respect to a given range of some performance indices. In this case, a clustering technique represents a powerful tool to deal with the problem. Main clusters of fuzzy controllers having similar behavior with respect to some performance indices are discovered. In order to precisely characterize rule bases and transform them to a quantifiable entity, transition between topological and numerical form of fuzzy rule bases is studied. Formulating a vector space structure and a base of relationships between fuzzy sets represents one of the main foci of the research. Adding logic parameters and defuzzification procedures to the formulated vectors is required to apply the clustering technique. In fact, this latter requires the existence of quantifiable fuzzy controllers. The obtained vectors are then treated by a fuzzy-neural clustering algorithm. Membership nuance to a cluster allows better legibility to evaluate relevance and relative interest of fuzzy controller parameters according to performance indices.