Signal compression and data compression are techniques for storing andtransmitting signals using fewer bits aspossible 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 proofsof these properties in a fuzzy environment.The proof of one-dimensionalmultiresolution analysis isgiven. 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 ,,)(,1,0(2RLF))(Rdecomposing the fuzzy signalis obtained.