# 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:

#### 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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2023-02-28

## How to Cite

Akakatshi Ossako, J.- louis, Walo Omana, R., Bopili Mbotia, R., & Kitombole Tshovu, A. (2023). Decomposition of A Fuzzy Function By One-Dimensional Fuzzy Multiresolution Analysis. Journal of Computing Research and Innovation, 8(1), 84–96. https://doi.org/10.24191/jcrinn.v8i1.336

## Section

General Computing  