We firstly review some fundamentals of fuzzy relation calculus and, by recalling some known results, we improve the mathematical contents of our previous papers by using the properties of a triangular norm over [0,1]. We make wide use of the theory of fuzzy relation equations for getting lossy compression and decompression of images interpreted as two-argument fuzzy matrices.The same scope is achieved by decomposing a fuzzy matrix using the concept of Schein rank. We illustrate two algorithms with a few examples.
Fuzzy Relation Calculus in the Compression and Decompression of Fuzzy Relations / W., Pedrycz; V., Loia; Sessa, Salvatore. - In: INTERNATIONAL JOURNAL OF IMAGE AND GRAPHICS. - ISSN 0219-4678. - STAMPA. - 2:4(2002), pp. 617-631. [10.1142/S0219467802000871]
Fuzzy Relation Calculus in the Compression and Decompression of Fuzzy Relations
SESSA, SALVATORE
2002
Abstract
We firstly review some fundamentals of fuzzy relation calculus and, by recalling some known results, we improve the mathematical contents of our previous papers by using the properties of a triangular norm over [0,1]. We make wide use of the theory of fuzzy relation equations for getting lossy compression and decompression of images interpreted as two-argument fuzzy matrices.The same scope is achieved by decomposing a fuzzy matrix using the concept of Schein rank. We illustrate two algorithms with a few examples.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
