Constructing a fuzzy controller from data

Fuzzy control can be interpreted as an approximation technique for a control function based on typical, imprecisely speciied input{output tuples that are represented by fuzzy sets. The imprecision is characterized by similarity relations that are induced by transformations of the canonical distance function between real numbers. Taking this interpretation of fuzzy controllers into account, in order to derive a fuzzy controller from observed data typical input{output tuples have to be identiied. In addition, a concept of similarity based on a transformations of the canonical distance is needed in order to characterize the typical input{output tuples by suitable fuzzy sets. A variety of fuzzy clustering algorithms exists that are exactly working in this spirit: They identify prototypes and assign fuzzy sets to the prototypes on the basis of a suitable transformed distance. In this paper we discuss how such fuzzy clustering techniques can be applied to construct a fuzzy controller from data and introduce special clustering algorithms that are tailored for this problem.