A Systematic Review on the Advancement in the Study of Fuzzy Variational Problems
The study of fuzzy variational problems has received significant attention over the past decade due to its successful applications in numerous fields, such as image segmentation and optimal control theory. The fuzzy Euler-Lagrange equations provide the necessary optimality conditions for solving fuz...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/8037562 |
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| _version_ | 1832567146708729856 |
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| author | Mansi Verma Chuei Yee Chen Adem Kılıçman Risman Mat Hasim |
| author_facet | Mansi Verma Chuei Yee Chen Adem Kılıçman Risman Mat Hasim |
| author_sort | Mansi Verma |
| collection | DOAJ |
| description | The study of fuzzy variational problems has received significant attention over the past decade due to its successful applications in numerous fields, such as image segmentation and optimal control theory. The fuzzy Euler-Lagrange equations provide the necessary optimality conditions for solving fuzzy variational problems explicitly and have been studied under several differentiability conditions. In this paper, we provide a systematic review to recap the history of variational principle in the calculus of variations and compare it with the existing techniques in the fuzzy setting. We begin with the preliminary concepts and definitions of fuzzy theory and scrutinize the Euler-Lagrange’s strategy via systematically searched studies concerning fuzzy variational problems to highlight the importance of improving the existing methods. Finally, we set up the main open problems regarding the limitations of the current approaches, shedding light on future directions. |
| format | Article |
| id | doaj-art-1553291f5c6e499ebd0693c070bef166 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-1553291f5c6e499ebd0693c070bef1662025-02-03T01:02:14ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/8037562A Systematic Review on the Advancement in the Study of Fuzzy Variational ProblemsMansi Verma0Chuei Yee Chen1Adem Kılıçman2Risman Mat Hasim3Department of Mathematics and StatisticsDepartment of Mathematics and StatisticsDepartment of Mathematics and StatisticsDepartment of Mathematics and StatisticsThe study of fuzzy variational problems has received significant attention over the past decade due to its successful applications in numerous fields, such as image segmentation and optimal control theory. The fuzzy Euler-Lagrange equations provide the necessary optimality conditions for solving fuzzy variational problems explicitly and have been studied under several differentiability conditions. In this paper, we provide a systematic review to recap the history of variational principle in the calculus of variations and compare it with the existing techniques in the fuzzy setting. We begin with the preliminary concepts and definitions of fuzzy theory and scrutinize the Euler-Lagrange’s strategy via systematically searched studies concerning fuzzy variational problems to highlight the importance of improving the existing methods. Finally, we set up the main open problems regarding the limitations of the current approaches, shedding light on future directions.http://dx.doi.org/10.1155/2022/8037562 |
| spellingShingle | Mansi Verma Chuei Yee Chen Adem Kılıçman Risman Mat Hasim A Systematic Review on the Advancement in the Study of Fuzzy Variational Problems Journal of Function Spaces |
| title | A Systematic Review on the Advancement in the Study of Fuzzy Variational Problems |
| title_full | A Systematic Review on the Advancement in the Study of Fuzzy Variational Problems |
| title_fullStr | A Systematic Review on the Advancement in the Study of Fuzzy Variational Problems |
| title_full_unstemmed | A Systematic Review on the Advancement in the Study of Fuzzy Variational Problems |
| title_short | A Systematic Review on the Advancement in the Study of Fuzzy Variational Problems |
| title_sort | systematic review on the advancement in the study of fuzzy variational problems |
| url | http://dx.doi.org/10.1155/2022/8037562 |
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