A fuzzy autoassociative morphological memory

Morphological associative memories are among several types of morphological neural network models which have been proposed over the course of the last few years. A neural network is called morphological if one of the fundamental operations of mathematical morphology, a dilation or an erosion, is performed at each node. These operations can be expressed as a max product or a min product in the mathematical theory of minimax algebra. This paper employs fuzzy set theory to generalize the operations "max product" and "min product" as used in binary autoassociative morphological memory (AMM) models. Replacing the original operations by new operations "fuzzy max product" and "fuzzy min product" in this setting yields a fuzzy AMM with crisp input patterns and fuzzy output patterns. A thresholding procedure can be applied to obtain crisp output patterns. This new approach significantly improves the error correction capability of binary autoassociative morphological memories.