The Kosko Subsethood Fuzzy Associative Memory (KS-FAM): Mathematical Background and Applications in Computer Vision

Abstract

Many well-known fuzzy associative memory (FAM) models can be viewed as (fuzzy) morphological neural networks (MNNs) because they perform an operation of (fuzzy) mathematical morphology at every node, possibly followed by the application of an activation function. The vast majority of these FAMs represent distributive models given by single-layer matrix memories. Although the Kosko subsethood FAM (KS-FAM) can also be classified as a fuzzy morphological associative memory (FMAM), the KS-FAM constitutes a two-layer non-distributive model. In this paper, we prove several theorems concerning the conditions of perfect recall, the absolute storage capacity, and the output patterns produced by the KS-FAM. In addition, we propose a normalization strategy for the training and recall phases of the KS-FAM. We employ this strategy to compare the error correction capabilities of the KS-FAM and other fuzzy and gray-scale associative memories in terms of some experimental results concerning gray-scale image reconstruction. Finally, we apply the KS-FAM to the task of vision-based self-localization in robotics.