title: Storage and recall capabilities of fuzzy morphological associative memories with adjunction-based learning.
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.
authors.affiliation: University of Londrina, Department of Mathematics, Londrina, PR, Brazil. valle@uel.br
authors.forename: Marcos Eduardo
authors.initials: ME
authors.lastname: Valle
authors.forename: Peter
authors.initials: P
authors.lastname: Sussner
mesh_terms: D003198:Computer Simulation; D017143:Fuzzy Logic; D006801:Humans; D016247:Information Storage and Retrieval; D007858:Learning / Q000502:physiology*; D008433:Mathematics; D011939:Mental Recall / Q000502:physiology*; D016571:Neural Networks, Computer