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 Kohonen-layer which receives fuzzy numbers as inputs and computes its output employing fuzzy weights. 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 for solving this problem. Furthermore, we formulate a fuzzified version of the standard learning rule, that can be applied on the fuzzified Kohonen neurons.