Data compression with fuzzy relational equations

This study focuses on fuzzy relational calculus viewed as a basis of data compression. Images are fuzzy relations. We investigate fuzzy relational equations as a basis of image compression. It is shown that both compression and decompression (reconstruction) phases are closely linked with the way in which fuzzy relational equations are developed and solved. The theoretical findings encountered in the theory of these equations are easily accommodated as the backbone of the relational compression. The character of the solutions to the equations makes them ideal for reconstruction purposes as they specify the extremal elements of the solution set and in such a way help establish some envelopes of the original images under compression. The flexibility of the conceptual and algorithmic framework arising there is also discussed. Numerical examples provide a suitable illustrative material emphasizing the main features of the compression mechanisms.