A decomposition of fuzzy relations

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

“…In Sect. 3, we confirm that the image decomposition experiments have computational times, with the proposed method, approximately diminished than 1=c with respect to the traditional method used in [10], ''c'' being the Schein rank of the fuzzy relation involved. Sect.…”

“…By using this traditional method in [10], we observe that if the learning rate a is higher, the above process can be completed for a shorter computation time but the result of the approximation is not good. If the learning rate a is lower, the same process requires larger computation time and the result of approximation is better.…”

“…A solution based on the gradient method has been presented in [10]. Since this method is iterative, we denote by ''iter'' the iteration step.…”

“…In this paper, two decomposition problems of a fuzzy relation are presented and related fast iterative methods, both based on the gradient algorithm, are proposed. The first problem concerns the decomposition of a fuzzy relation using the concept of Schein rank [1,2,4] and an its solution has been proposed in [9][10]. In Sect.…”

“…In Sect. 2, we slightly transform the derivatives in the traditional gradient algorithm, used in [10], for obtaining a new fast method, based also on the simultaneous updating of the prototype fuzzy relation. In Sect.…”