On the Output Behaviour of Fuzzified Kohonen Nets

W.-M. Lippe, S. Niendieck, and U. Sprekelmeyer (Germany)


fuzzy-sets, fuzzified kohonen nets, fuzzified self organazing-map, goodness prediction


Several ways of combining concepts of fuzzy set theory with connectionist methods are known. We focus on the use of fuzzy numbers in neural networks. Our goal is to create a fully fuzzified Self-Organizing-Map, which receives fuzzy numbers as inputs and computes its output employing fuzzy weights. We want to extend results about good ness prediction, that exist for fuzzified multilayer perceptrons (MLP). The main problem is the determination of the winning neuron by the exclusive use of special, “monotonic” fuzzy operations, which guarantee a certain “goodness” of the in put/output behaviour. A selection-function is introduced, solving this problem. Further on we formulate a fuzzified version of the standard learning rule, that can be applied on the fuzzified Kohonen neurons.

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