PROBABILISTIC SETS IN IDENTIFICATION OF FUZZY SYSTEMS.

We discuss fuzzy relational equation as a formal model of many processes (e. g. medical diagnosis) and present the identification procedure leading to obtain the parameters of the model (fuzzy relation). The method discussed is based on ideas of fuzzy relational equation, probabilistic sets forming an extension of fuzzy set and clustering techniques. First in the paper the idea of probabilistic sets is outlined and next the discussion is focused on several results on identification e. g. the way of estimating a fuzzy relation and choosing the best collection of input sets of the model. Identification algorithm is illustrated by means of numerical examples pointing out the usefulness of the notion of probabilistic sets.