fuzzy associative memory, fuzzy preorder, eigen fuzzy sets, formal concept analysis, erosion, dilation

A novel theoretical background of fuzzy associative memories (FAM) is proposed. A framework of formal concept analysis is used for a new working theory of FAM. Two principal activities of FAM are formalized : data retrieval and noise reduction. It is shown that the problem of data retrieval is connected with solvability and eigen sets of a certain system of fuzzy relation equations. The differentiation of FAM models according to their ability to reduce noise is defined. It is shown how the choice of formal context determines a type of noise that can be reduced by the corresponding retrieval mechanism. Finally, we propose a fast algorithm of data retrieval.