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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: Verma, Mansi, Chuei, Yee Chen, Kılıçman, Adem, Mat Hasim, Risman
Format: Article
Published: Hindawi 2022
Online Access:http://psasir.upm.edu.my/id/eprint/100474/
https://www.hindawi.com/journals/jfs/2022/8037562/
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spelling my.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
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
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
author Verma, Mansi
Chuei, Yee Chen
Kılıçman, Adem
Mat Hasim, Risman
spellingShingle Verma, Mansi
Chuei, Yee Chen
Kılıçman, Adem
Mat Hasim, Risman
A systematic review on the advancement in the study of fuzzy variational problems
author_facet Verma, Mansi
Chuei, Yee Chen
Kılıçman, Adem
Mat Hasim, Risman
author_sort Verma, Mansi
title 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_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_sort systematic review on the advancement in the study of fuzzy variational problems
publisher Hindawi
publishDate 2022
url http://psasir.upm.edu.my/id/eprint/100474/
https://www.hindawi.com/journals/jfs/2022/8037562/
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score 13.211869

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