A relationship between binary morphological autoassociative memories and fuzzy set theory

Morphological neural networks (MNN) are a class of artificial neural networks whose operations are derived from mathematical morphology. In a morphological neural net, the usual sum of weighted inputs is replaced by a maximum or minimum of weighted inputs (in this context, the weighting is performed by summing the weight and the input). We speak of a max product, a min product respectively. The emphasis of this paper is on morphological associative memories (MAM), in particular on binary autoassociative morphological memories (AMM). We give a new set theoretic interpretation of recording and recall in binary AMM and provide a generalization using fuzzy set theory