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

  • Authors:

  • H. Nobuhara;W. Pedrycz;K. Hirota

  • Affiliations:

  • Dept. of Comput. Intelligence & Syst. Sci., Tokyo Inst. of Technol.;-;-

  • Venue:
  • IEEE Transactions on Fuzzy Systems
  • Year:
  • 2000

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Abstract

A fast solving method of the solution for max continuous t-norm composite fuzzy relational equation of the type G(i, j)=(RT□Ai)T□Bj , i=1, 2, ..., I, j=1, 2, ..., J, where Ai∈F(X)X={x1, x2, ..., xM }, Bj∈F(Y) Y={y1, y2, ..., yN}, 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