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Fuzzy transforms: theory and applications. (English) Zbl 1092.41022
In this paper the technique of the direct and inverse fuzzy transform is introduced and approximation properties of the inverse fuzzy transform are established. Two new fuzzy transforms based on operations of a residuated lattice on \([0,1]\) are introduced. These new lattice fuzzy transforms lead to new approximation models. Three types of the inverse fuzzy transforms are compared. A method of lossy image compression and reconstruction on the basis of the fuzzy transform is presented as an application.

MSC:
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
68P30 Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science)
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