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

Jean-louis Akakatshi Ossako; Rebecca Walo Omana; Richard Bopili Mbotia; Antoine Kitombole  Tshovu

doi:10.24191/jcrinn.v8i1.336

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

Authors

Jean-louis Akakatshi Ossako Department of Mathematics, Statistics and Computer Science, Faculty of Science and Technology, University of Kinshasa
Rebecca Walo Omana Department of Mathematics, Statistics and Computer Science, Faculty of Science and Technology, University of Kinshasa
Richard Bopili Mbotia Department of Physics, Faculty of Science and Technology, University of Kinshasa
Antoine Kitombole Tshovu Department of Mathematics, Statistics and Computer Science, Faculty of Science and Technology, University of Kinshasa

DOI:

https://doi.org/10.24191/jcrinn.v8i1.336

Keywords:

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

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.

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