Fast solving method of fuzzy relational equation and its application to lossy image compression/reconstruction

A fast solving method of the greatest solution for max continuous t-norm co mposite fuzzy relational equation of the type G(i, j) = (R-T square A(i))(T ) square B-j, i = 1, 2,..., I, j = 1, 2,...,J, where A(i) is an element of F(X) X = {x(1),x(2),...,x(M)}, B-j is an element of F(Y) Y = {y(1),y(2),... ,y(N)}, R is an element of F(X x Y), and square: max continuous t-norm comp osition, Is proposed. It decreases the computation time IJMN(L + T + P) to JM(I + N)(L + P), where L, T, and P denote the computation time of min, t-n orm, and relative pseudocomplement operations, respectively, by simplifying the conventional reconstruction equation based on the properties of t-norm and relative pseudocomplement. The method is applied to a lossy image comp ression and reconstruction problem, where it is confirmed that the computat ion time of the reconstructed image is decreased to 1/335.6 the compression rate being 0.0351, and it achieves almost equivalent performance for the c onventional lossy image compression methods based on discrete cosine transf orm and vector quantization.