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This paper presents the design of an accurate fuzzy dependency approximator that uses fuzzy inputs, fuzzy targets and fuzzy weights. The proposed design can cope with arbitrarily discrete membership functions. It is a combination between a Kohonen network used for clustering the fuzzy data and a set of low degree rational fuzzy approximators. The self-organizing system works in fuzzy arithmetic and uses a specific training strategy that combines fuzzy and defuzzified data streams. A genetic algorithm trains the rational fuzzy approximators by using the local fuzzy data cluster. The performance of the piecewise rational fuzzy approximator is experimentally evaluated and compared with other types of techniques for approximating fuzzy dependencies with regard to the achieved accuracy and the required computing time.