Recurrent exponential fuzzy associative memories (RE-FAMs) are non-distributive memory models derived from the multivalued exponential recurrent associative memory (MERAM) of Chiueh and Tsai. A RE-FAM defines recursively a sequence of fuzzy sets obtained by a weighted average of the fundamental memories. In this paper, we show that the output of a single-step RE-FAM can be made as close as desired to a certain convex combination of the fundamental memories most similar to the input. This paper also addresses the storage and recall capability of RE-FAMs. Precisely, computational experiments reveal that RE-FAMs can be effectively used for the retrieval of gray-scale images corrupted by either Gaussian noise or salt and pepper noise.
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