Modified Block Homotopy Perturbation Method for solving triangular linear Diophantine fuzzy system of equations
Numerous real-world applications can be solved using the broadly adopted notions of intuitionistic fuzzy sets, Pythagorean fuzzy sets, and q-rung orthopair fuzzy sets. These theories, however, have their own restrictions in terms of membership and non-membership levels. Because it utilizes benchmark...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SAGE Publishing
2023-03-01
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| Series: | Advances in Mechanical Engineering |
| Online Access: | https://doi.org/10.1177/16878132231159519 |
| _version_ | 1797867430357237760 |
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| author | Mudassir Shams Nasreen Kausar Naveed Khan Mohd Asif Shah |
| author_facet | Mudassir Shams Nasreen Kausar Naveed Khan Mohd Asif Shah |
| author_sort | Mudassir Shams |
| collection | DOAJ |
| description | Numerous real-world applications can be solved using the broadly adopted notions of intuitionistic fuzzy sets, Pythagorean fuzzy sets, and q-rung orthopair fuzzy sets. These theories, however, have their own restrictions in terms of membership and non-membership levels. Because it utilizes benchmark or control parameters relating to membership and non-membership levels, this theory is particularly valuable for modeling uncertainty in real-world problems. We propose the unique concept of linear Diophantine fuzzy set with benchmark parameters to overcome these restrictions. Different numerical, analytical, and semi-analytical techniques are used to solve linear systems of equations with several fuzzy numbers, such as intuitionistic fuzzy number, triangular fuzzy number, bipolar fuzzy number, trapezoidal fuzzy number, and hexagon fuzzy number. The purpose of this research is to solve a fuzzy linear system of equations with the most generalized fuzzy number, such as Triangular linear Diophantine fuzzy number, using an analytical technique called Homotopy Perturbation Method. The linear systems co-efficient are crisp when the right hand side vector is a triangular linear Diophantine fuzzy number. A numerical test examples demonstrates how our newly improved analytical technique surpasses other existing methods in terms of accuracy and CPU time. The triangular linear Diophantine fuzzy systems of equations’ strong and weak visual representations are explored. |
| first_indexed | 2024-04-09T23:41:10Z |
| format | Article |
| id | doaj.art-01ac6a22263a4d31948623520d3679fd |
| institution | Directory Open Access Journal |
| issn | 1687-8140 |
| language | English |
| last_indexed | 2024-04-09T23:41:10Z |
| publishDate | 2023-03-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Advances in Mechanical Engineering |
| spelling | doaj.art-01ac6a22263a4d31948623520d3679fd2023-03-18T14:15:03ZengSAGE PublishingAdvances in Mechanical Engineering1687-81402023-03-011510.1177/16878132231159519Modified Block Homotopy Perturbation Method for solving triangular linear Diophantine fuzzy system of equationsMudassir Shams0Nasreen Kausar1Naveed Khan2Mohd Asif Shah3Department of Mathematics and Statistics, Riphah International University, Islamabad, PakistanDeperament of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Istanbul, TurkeyDepartment of Mathematics and Statistics, Riphah International University, Islamabad, PakistanDepartment of Economics, College of Business and Economics, Kebri Dehar University, Kebri Dahar, EthiopiaNumerous real-world applications can be solved using the broadly adopted notions of intuitionistic fuzzy sets, Pythagorean fuzzy sets, and q-rung orthopair fuzzy sets. These theories, however, have their own restrictions in terms of membership and non-membership levels. Because it utilizes benchmark or control parameters relating to membership and non-membership levels, this theory is particularly valuable for modeling uncertainty in real-world problems. We propose the unique concept of linear Diophantine fuzzy set with benchmark parameters to overcome these restrictions. Different numerical, analytical, and semi-analytical techniques are used to solve linear systems of equations with several fuzzy numbers, such as intuitionistic fuzzy number, triangular fuzzy number, bipolar fuzzy number, trapezoidal fuzzy number, and hexagon fuzzy number. The purpose of this research is to solve a fuzzy linear system of equations with the most generalized fuzzy number, such as Triangular linear Diophantine fuzzy number, using an analytical technique called Homotopy Perturbation Method. The linear systems co-efficient are crisp when the right hand side vector is a triangular linear Diophantine fuzzy number. A numerical test examples demonstrates how our newly improved analytical technique surpasses other existing methods in terms of accuracy and CPU time. The triangular linear Diophantine fuzzy systems of equations’ strong and weak visual representations are explored.https://doi.org/10.1177/16878132231159519 |
| spellingShingle | Mudassir Shams Nasreen Kausar Naveed Khan Mohd Asif Shah Modified Block Homotopy Perturbation Method for solving triangular linear Diophantine fuzzy system of equations Advances in Mechanical Engineering |
| title | Modified Block Homotopy Perturbation Method for solving triangular linear Diophantine fuzzy system of equations |
| title_full | Modified Block Homotopy Perturbation Method for solving triangular linear Diophantine fuzzy system of equations |
| title_fullStr | Modified Block Homotopy Perturbation Method for solving triangular linear Diophantine fuzzy system of equations |
| title_full_unstemmed | Modified Block Homotopy Perturbation Method for solving triangular linear Diophantine fuzzy system of equations |
| title_short | Modified Block Homotopy Perturbation Method for solving triangular linear Diophantine fuzzy system of equations |
| title_sort | modified block homotopy perturbation method for solving triangular linear diophantine fuzzy system of equations |
| url | https://doi.org/10.1177/16878132231159519 |
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