Abstract
We examine the principle capabilities and limits of fuzzy classifiers that are based on a finite set of fuzzy if-then rules like they are used for fuzzy controllers, except that the conclusion of a rule specifies a discrete class instead of a (fuzzy) real output value. Our results show that in the two-dimensional case, for classification problems whose solutions can only be solved approximately by crisp classification rules, very simple fuzzy rules provide an exact solution. However, in the multi-dimensional case, even for linear separable problems, max-min rules are not sufficient.
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Klawonn, F., Klement, EP. (1997). Mathematical analysis of fuzzy classifiers. In: Liu, X., Cohen, P., Berthold, M. (eds) Advances in Intelligent Data Analysis Reasoning about Data. IDA 1997. Lecture Notes in Computer Science, vol 1280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0052854
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DOI: https://doi.org/10.1007/BFb0052854
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