TY - JOUR
T1 - Fast solving method of fuzzy relational equation and its application to lossy image compression/reconstruction
AU - Nobuhara, Hajime
AU - Pedrycz, Witold
AU - Hirota, Kaoru
PY - 2000/6
Y1 - 2000/6
N2 - A fast solving method of the greatest solution for max continuous t-norm composite fuzzy relational equation of the type G(i,j) = (R T□A i) T□B j, i = 1,2,···,I,j = 1,2,···,J, where A i∈F(X) X = {x 1,x 2,···,x M}, B j∈F(Y) Y = {y 1,y 2,···,y N}, R∈F(X×Y), and □: max continuous t-norm composition, 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-norm, 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 compression and reconstruction problem, where it is confirmed that the computation 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 conventional lossy image compression methods based on discrete cosine transform and vector quantization.
AB - A fast solving method of the greatest solution for max continuous t-norm composite fuzzy relational equation of the type G(i,j) = (R T□A i) T□B j, i = 1,2,···,I,j = 1,2,···,J, where A i∈F(X) X = {x 1,x 2,···,x M}, B j∈F(Y) Y = {y 1,y 2,···,y N}, R∈F(X×Y), and □: max continuous t-norm composition, 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-norm, 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 compression and reconstruction problem, where it is confirmed that the computation 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 conventional lossy image compression methods based on discrete cosine transform and vector quantization.
UR - http://www.scopus.com/inward/record.url?scp=0034204784&partnerID=8YFLogxK
U2 - 10.1109/91.855920
DO - 10.1109/91.855920
M3 - Article
AN - SCOPUS:0034204784
SN - 1063-6706
VL - 8
SP - 325
EP - 334
JO - IEEE Transactions on Fuzzy Systems
JF - IEEE Transactions on Fuzzy Systems
IS - 3
ER -