Fuzzy Hilbert Transform of Fuzzy Functions
This paper studies the properties of the Fourier transform of the fuzzy function, and extends the classical Poisson integral formula on the half plane to the fuzzy case, obtaining the composition of the fuzzy set generated by a point in the complex field under the action of the fuzzy function. Furth...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/2/289 |
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| author | Zhibo Yan |
| author_facet | Zhibo Yan |
| author_sort | Zhibo Yan |
| collection | DOAJ |
| description | This paper studies the properties of the Fourier transform of the fuzzy function, and extends the classical Poisson integral formula on the half plane to the fuzzy case, obtaining the composition of the fuzzy set generated by a point in the complex field under the action of the fuzzy function. Further, we define and study the fuzzy Hilbert transform of fuzzy functions and their properties. We prove that when the fuzzy function degenerates to the classical case, the fuzzy Hilbert transform will degenerate to the classical Hilbert transform, which proves that the fuzzy Hilbert transform is an extension of classical transformations in the fuzzy function space. In addition, we point out and prove some properties of the fuzzy Hilbert transform. For some fuzzy functions that meet certain requirements, their fuzzy Hilbert transform is a fuzzy point on 0. |
| format | Article |
| id | doaj-art-a9a574da9632401a9f00e58de829bae9 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-a9a574da9632401a9f00e58de829bae92025-01-24T13:40:03ZengMDPI AGMathematics2227-73902025-01-0113228910.3390/math13020289Fuzzy Hilbert Transform of Fuzzy FunctionsZhibo Yan0School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, ChinaThis paper studies the properties of the Fourier transform of the fuzzy function, and extends the classical Poisson integral formula on the half plane to the fuzzy case, obtaining the composition of the fuzzy set generated by a point in the complex field under the action of the fuzzy function. Further, we define and study the fuzzy Hilbert transform of fuzzy functions and their properties. We prove that when the fuzzy function degenerates to the classical case, the fuzzy Hilbert transform will degenerate to the classical Hilbert transform, which proves that the fuzzy Hilbert transform is an extension of classical transformations in the fuzzy function space. In addition, we point out and prove some properties of the fuzzy Hilbert transform. For some fuzzy functions that meet certain requirements, their fuzzy Hilbert transform is a fuzzy point on 0.https://www.mdpi.com/2227-7390/13/2/289fuzzy functionfuzzy Fourier transformPoisson integral formulafuzzy Hilbert transform |
| spellingShingle | Zhibo Yan Fuzzy Hilbert Transform of Fuzzy Functions Mathematics fuzzy function fuzzy Fourier transform Poisson integral formula fuzzy Hilbert transform |
| title | Fuzzy Hilbert Transform of Fuzzy Functions |
| title_full | Fuzzy Hilbert Transform of Fuzzy Functions |
| title_fullStr | Fuzzy Hilbert Transform of Fuzzy Functions |
| title_full_unstemmed | Fuzzy Hilbert Transform of Fuzzy Functions |
| title_short | Fuzzy Hilbert Transform of Fuzzy Functions |
| title_sort | fuzzy hilbert transform of fuzzy functions |
| topic | fuzzy function fuzzy Fourier transform Poisson integral formula fuzzy Hilbert transform |
| url | https://www.mdpi.com/2227-7390/13/2/289 |
| work_keys_str_mv | AT zhiboyan fuzzyhilberttransformoffuzzyfunctions |