Two iterative methods of decomposition of a fuzzy relation for image compression/decompression processing

A decomposition problem of max–min type for a fuzzy relation is proposed. A fast method is derived by transforming slightly the derivatives in the traditional gradient algorithm and by updating simultaneously the prototype relation. The complexities of the proposed algorithm, with respect to the traditional gradient one, are decreased to approximately 1=c, where ‘‘c’’ denotes the Schein rank of the fuzzy relation involved. A dual decomposition problem of max–min type is also formulated and a similar fast method is presented. Both methods are applied to image compression/decompression processing.