Fuzzy Associative Memories and Their Relationship to Mathematical Morphology

Fuzzy associative memories (FAMs) belong to the class of fuzzy neural networks (FNNs). A FNN is an artificial neural network (ANN) whose input patterns, output patterns, and/or connection weights are fuzzy-valued [19, 11]. Research on FAM models originated in the early 1990’s with the advent of Kosko’s FAM [35, 37]. Like many other associative memory models, Kosko’s FAM consists of a single-layer feedforward FNN that stores the fuzzy rule “If x is Xk then y is Yk” using a fuzzy Hebbian learning rule in terms of max-min or max-product compositions for the synthesis of its weight matrix W . Despite successful applications of Kosko’s FAMs to problems such as backing up a truck and trailer [35], target tracking [37], and voice cell control in ATM networks [44], Kosko’s FAM suffers from an extremely low storage capacity of one rule per FAM matrix. Therefore, Kosko’s overall