Decomposition of A Fuzzy Function By One-Dimensional Fuzzy Multiresolution Analysis

Abstract

Signal compression and data compression are techniques for storing and transmitting signals using fewer bits as possible for encoding a complete signal. A good signal compression scheme requires a good signal decomposition scheme. The decomposition of the signal can be done as follows: The signal is split into a low-resolution part, described by a smaller number of samples than the original signal, and a signal difference, which describes the difference between the low-resolution signal and the real coded signal. Our paper deals with the proofs of these properties in a fuzzy environment. The proof of one- dimensional multiresolution analysis is given. The concept of fuzzy wavelets is introduced and as a byproduct a special fuzzy space of details of a signal is given and an orthonormal basis of Fdecomposing the fuzzy signal is obtained.

Keywords

• Fuzzy image
• fuzzy multiresolution analyzes
• fuzzy basis functions
• fuzzy basis Riesz
• fuzzy orthonormal basis