BETA NEURO-FUZZY SYSTEMS
In this paper we present the Beta function and its main properties. A key feature of the Beta function, which is given by the central limit theorem, is also shown. We then introduce a new category of neural networks based on a new kernel: the Beta function. Next, we investigate the use of Beta fuzz...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Gdańsk University of Technology
2003-01-01
|
| Series: | TASK Quarterly |
| Subjects: | |
| Online Access: | https://journal.mostwiedzy.pl/TASKQuarterly/article/view/2209 |
| _version_ | 1828284870336446464 |
|---|---|
| author | ADEL M. ALIMI |
| author_facet | ADEL M. ALIMI |
| author_sort | ADEL M. ALIMI |
| collection | DOAJ |
| description |
In this paper we present the Beta function and its main properties. A key feature of the Beta function, which is given by the central limit theorem, is also shown. We then introduce a new category of neural networks based on a new kernel: the Beta function. Next, we investigate the use of Beta fuzzy basis functions for the design of fuzzy logic systems. The functional equivalence between Beta-based function neural networks and Beta fuzzy logic systems is then shown with the introduction of Beta neuro-fuzzy systems. By using the Stone-Weierstrass theorem and expanding the output of the Beta neuro-fuzzy system into a series of Beta fuzzy-based functions, we prove that one can uniformly approximate any real continuous function on a compact set to any arbitrary accuracy. Finally, a learning algorithm of the Beta neuro-fuzzy system is described and illustrated with numerical examples.
|
| first_indexed | 2024-04-13T09:07:16Z |
| format | Article |
| id | doaj.art-fb79c1eb48c944d5a1202a67ed5e5faf |
| institution | Directory Open Access Journal |
| issn | 1428-6394 |
| language | English |
| last_indexed | 2024-04-13T09:07:16Z |
| publishDate | 2003-01-01 |
| publisher | Gdańsk University of Technology |
| record_format | Article |
| series | TASK Quarterly |
| spelling | doaj.art-fb79c1eb48c944d5a1202a67ed5e5faf2022-12-22T02:52:57ZengGdańsk University of TechnologyTASK Quarterly1428-63942003-01-0171BETA NEURO-FUZZY SYSTEMSADEL M. ALIMI0University of Sfax, Research Group on Intelligent Machines, National School of Engineers ENIS, Department of Electrical Engineering In this paper we present the Beta function and its main properties. A key feature of the Beta function, which is given by the central limit theorem, is also shown. We then introduce a new category of neural networks based on a new kernel: the Beta function. Next, we investigate the use of Beta fuzzy basis functions for the design of fuzzy logic systems. The functional equivalence between Beta-based function neural networks and Beta fuzzy logic systems is then shown with the introduction of Beta neuro-fuzzy systems. By using the Stone-Weierstrass theorem and expanding the output of the Beta neuro-fuzzy system into a series of Beta fuzzy-based functions, we prove that one can uniformly approximate any real continuous function on a compact set to any arbitrary accuracy. Finally, a learning algorithm of the Beta neuro-fuzzy system is described and illustrated with numerical examples. https://journal.mostwiedzy.pl/TASKQuarterly/article/view/2209beta functionkernel based neural networksSugeno fuzzy modelneuro-fuzzy systemsuniversal approximation propertylearning algorithms |
| spellingShingle | ADEL M. ALIMI BETA NEURO-FUZZY SYSTEMS TASK Quarterly beta function kernel based neural networks Sugeno fuzzy model neuro-fuzzy systems universal approximation property learning algorithms |
| title | BETA NEURO-FUZZY SYSTEMS |
| title_full | BETA NEURO-FUZZY SYSTEMS |
| title_fullStr | BETA NEURO-FUZZY SYSTEMS |
| title_full_unstemmed | BETA NEURO-FUZZY SYSTEMS |
| title_short | BETA NEURO-FUZZY SYSTEMS |
| title_sort | beta neuro fuzzy systems |
| topic | beta function kernel based neural networks Sugeno fuzzy model neuro-fuzzy systems universal approximation property learning algorithms |
| url | https://journal.mostwiedzy.pl/TASKQuarterly/article/view/2209 |
| work_keys_str_mv | AT adelmalimi betaneurofuzzysystems |