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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| Format: | Article |
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Hindawi
2022
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| _version_ | 1796983901245145088 |
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| author | Verma, Mansi Chuei, Yee Chen Kılıçman, Adem Mat Hasim, Risman |
| author_facet | Verma, Mansi Chuei, Yee Chen Kılıçman, Adem Mat Hasim, Risman |
| author_sort | Verma, Mansi |
| collection | UPM |
| 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. |
| first_indexed | 2024-03-06T11:12:56Z |
| format | Article |
| id | upm.eprints-100474 |
| institution | Universiti Putra Malaysia |
| last_indexed | 2024-03-06T11:12:56Z |
| publishDate | 2022 |
| publisher | Hindawi |
| record_format | dspace |
| spelling | upm.eprints-1004742023-12-15T03:05:32Z http://psasir.upm.edu.my/id/eprint/100474/ A systematic review on the advancement in the study of fuzzy variational problems Verma, Mansi Chuei, Yee Chen Kılıçman, Adem Mat Hasim, Risman 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. Hindawi 2022-02-07 Article PeerReviewed Verma, Mansi and Chuei, Yee Chen and Kılıçman, Adem and Mat Hasim, Risman (2022) A systematic review on the advancement in the study of fuzzy variational problems. Journal of Function Spaces, 2022. art. no. 8037562. pp. 1-14. ISSN 2314-8896; ESSN: 2314-8888 https://www.hindawi.com/journals/jfs/2022/8037562/ 10.1155/2022/8037562 |
| spellingShingle | Verma, Mansi Chuei, Yee Chen Kılıçman, Adem Mat Hasim, Risman A systematic review on the advancement in the study of fuzzy variational problems |
| 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 |
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