Generalizing Operations of Binary Autoassociative Morphological Memories Using Fuzzy Set Theory

  • Authors:
  • Peter Sussner

  • Affiliations:
  • Institute of Mathematics, Statistics, and Scientific Computing, State University of Campinas, Campinas, CEP13081-970, SP, Brazil. sussner@ime.unicamp.br

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2003

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Abstract

Morphological neural networks (MNNs) are a class of artificial neural networks whose operations can be expressed in the mathematical theory of minimax algebra. 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.In recent years, a number of different MNN models and applications have emerged. The emphasis of this paper is on morphological associative memories (MAMs), in particular on binary autoassociative morphological memories (AMMs). We give a new set theoretic interpretation of recording and recall in binary AMMs and provide a generalization using fuzzy set theory.