On the combination of fuzzy logic and Kohonen nets

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 goodness 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 input/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