Fuzzy Notions in Nonlinear System Classification

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Abstract
Pattern Recognition methods like the A-nearest neighbor technique and clustering have been successfully used to classify nonlinear systems to a predetermined set of well separated classes, demonstrating similarities in their input-output behavior. The cross-correlation function has been used as a feature vector which yielded a classification with a relatively small misclassification error. Further categorization of the nonlinearity within a class is not possible through the above approach. However, a membership factor in a fuzzy sense can be assigned to each nonlinear system within a certain class. This factor is dependent on the coefficients of the polynomial expansion of the nonlinearity involved and may be obtained through the cross-correlation vector. This way, every class of nonlinear systems may be defined as a fuzzy set. The investigation of the properties of such a set as well as its contribution to the further classification of nonlinear systems is discussed in this paper.

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