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

Tunable equivalence fuzzy associative memories

“…for some similarity measure SM on F(X) in the original definition above [49], then we speak of a weighted similarity measure fuzzy associative memory, for short a weighted SM-FAM [1,2,44].…”

“…Previous publications on -FAMs have focused on the cases where the functions ξ are given by fuzzy subsethood or similarity measures, leading to (weighted) subsethood, dual subsethood, and similarity measure FAMs [1,2]. These models, referred to using the acronyms S-FAMs, dual S-FAMs, and SM-FAMs (or weighted S-FAMs, dual S-FAMS, and SM-FAMs if one wishes to stress the inclusion of adjustable weights in their first layers), have found inspiration in fuzzy mathematical morphology (FMM) [3][4][5][6].…”

An introduction to morphological associative memories in complete lattices and inf-semilattices

“…We considered the ten gray-scale images of size 64 × 64 with 256 gray levels (downsized versions of images of size 256 × 256 1 ) that are depicted in Figure 1. In addition, we compared M r to other distributive fuzzy and neural associative memory models that had recently been applied to a similar problem [14].…”

“…MAMs including fuzzy morphological associative memories (FMAMs) have been extensively analyzed and applied to a variety problems such as pattern recognition and classification [3], [11], prediction [12], vision-based self-localization in robotics [14], [15], image compression [16], color image segmentation [17], and hyperspectral image analysis [18]. The characteristics of the autoassociative morphological memories (AMMs) W XX and M XX include optimal absolute storage capacity and one-step convergence [2], [3].…”

Generalized Recurrent Exponential Fuzzy Associative Memories Based on Similarity Measures

“…Besides a very high storage capacity, the ECAM exhibits an excellent error correction capability but -like the discrete Hopfield network -the ECAM is only suited for storing and recalling bipolar patterns. However, many applications of AMs, including the retrieval of gray-scale images in the presence of noise, require the storage and recall of many-valued patterns such as realvalued vectors, complex-valued vectors, or fuzzy sets [5,6,7,8,9,10,11].…”