Identification of functional fuzzy models using multidimensional reference fuzzy sets

Most commonly, fuzzy systems for modelling and control use one-dimensional orthogonal reference fuzzy sets such as triangular or trapezoidal ones. In this article a new description of functional fuzzy models by fuzzy rules with premises evaluating point affinities is presented. This results in multidimensional reference fuzzy sets. An algorithm to identify such systems using cluster algorithms is proposed. Two algorithms, the fuzzy-c-means and the Gustafson-and-Kessel algorithm with locally varying distance measures, are applied. The performance of the identification algorithm is demonstrated by applying it to the identification of two nonlinear systems. One of them is a gas furnace described by the well known Box-Jenkins data.