Storage and recall capabilities of fuzzy morphological associative memories with adjunction-based learning

  • Authors:

  • Marcos Eduardo Valle;Peter Sussner

  • Affiliations:

  • University of Londrina, Department of Mathematics, Londrina, PR 86055-900, Brazil;University of Campinas, Department of Applied Mathematics, Campinas, SP 13083-859, Brazil

  • Venue:
  • Neural Networks
  • Year:
  • 2011

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Abstract

We recently employed concepts of mathematical morphology to introduce fuzzy morphological associative memories (FMAMs), a broad class of fuzzy associative memories (FAMs). We observed that many well-known FAM models can be classified as belonging to the class of FMAMs. Moreover, we developed a general learning strategy for FMAMs using the concept of adjunction of mathematical morphology. In this paper, we describe the properties of FMAMs with adjunction-based learning. In particular, we characterize the recall phase of these models. Furthermore, we prove several theorems concerning the storage capacity, noise tolerance, fixed points, and convergence of auto-associative FMAMs. These theorems are corroborated by experimental results concerning the reconstruction of noisy images. Finally, we successfully employ FMAMs with adjunction-based learning in order to implement fuzzy rule-based systems in an application to a time-series prediction problem in industry.