Gauss-Seidel and Sor Methods for Solving Intuitionistic Fuzzy System of Linear Equations
Solving various real-life problems ultimately requires solving systems of linear equations. However, the parameters involved in such real-life problems may be pervaded with uncertainty, which results in fuzzy parameters rather than crisp parameters. Intuitionistic fuzzy parameters are more suitable...
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MDPI AG
2023-04-01
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| Series: | Computer Sciences & Mathematics Forum |
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| Online Access: | https://www.mdpi.com/2813-0324/7/1/47 |
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| author | Bidhan Chandra Saw Sushanta Man Anupama Bairagi Subhendu Bikash Hazra |
| author_facet | Bidhan Chandra Saw Sushanta Man Anupama Bairagi Subhendu Bikash Hazra |
| author_sort | Bidhan Chandra Saw |
| collection | DOAJ |
| description | Solving various real-life problems ultimately requires solving systems of linear equations. However, the parameters involved in such real-life problems may be pervaded with uncertainty, which results in fuzzy parameters rather than crisp parameters. Intuitionistic fuzzy parameters are more suitable for some cases, since they allow us to tackle the feeling of fear or hesitation when making a decision. These are characteristics of human beings that occur when applying knowledge and skills. The intuitionistic fuzzy linear system (IFLS) resulting from real-life problem involves large number of equations and equally large number of unknowns. When IFLS is in matrix-vector form, the resulting coefficient matrix will have a sparse structure, which makes iterative methods necessary for their solution. In this paper, the known Gauss–Seidel and SOR iterative methods for solving linear system of equations are discussed, to the best of our knowledge for the first time, to solve (IFLS). The single parametric form representation of intuitionistic fuzzy numbers (IFN) makes it possible to apply these iterative techniques to IFLS. Finally, a problem of voltage input output in an electric circuit has been considered to show the applicability and the efficiency of these methods. |
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| format | Article |
| id | doaj.art-404af2475b6b4a3891a553be36a7f565 |
| institution | Directory Open Access Journal |
| issn | 2813-0324 |
| language | English |
| last_indexed | 2024-03-08T20:51:36Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
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| series | Computer Sciences & Mathematics Forum |
| spelling | doaj.art-404af2475b6b4a3891a553be36a7f5652023-12-22T14:02:10ZengMDPI AGComputer Sciences & Mathematics Forum2813-03242023-04-01714710.3390/IOCMA2023-14437Gauss-Seidel and Sor Methods for Solving Intuitionistic Fuzzy System of Linear EquationsBidhan Chandra Saw0Sushanta Man1Anupama Bairagi2Subhendu Bikash Hazra3Department of Mathematics, Bankura University, Bankura 722155, West Bengal, IndiaDepartment of Mathematics, Bankura University, Bankura 722155, West Bengal, IndiaDepartment of Mathematics, Bankura University, Bankura 722155, West Bengal, IndiaDepartment of Mathematics, Bankura University, Bankura 722155, West Bengal, IndiaSolving various real-life problems ultimately requires solving systems of linear equations. However, the parameters involved in such real-life problems may be pervaded with uncertainty, which results in fuzzy parameters rather than crisp parameters. Intuitionistic fuzzy parameters are more suitable for some cases, since they allow us to tackle the feeling of fear or hesitation when making a decision. These are characteristics of human beings that occur when applying knowledge and skills. The intuitionistic fuzzy linear system (IFLS) resulting from real-life problem involves large number of equations and equally large number of unknowns. When IFLS is in matrix-vector form, the resulting coefficient matrix will have a sparse structure, which makes iterative methods necessary for their solution. In this paper, the known Gauss–Seidel and SOR iterative methods for solving linear system of equations are discussed, to the best of our knowledge for the first time, to solve (IFLS). The single parametric form representation of intuitionistic fuzzy numbers (IFN) makes it possible to apply these iterative techniques to IFLS. Finally, a problem of voltage input output in an electric circuit has been considered to show the applicability and the efficiency of these methods.https://www.mdpi.com/2813-0324/7/1/47parametric form of intuitionistic fuzzy numberintuitionistic fuzzy linear system (IFLS)Gauss–Seidel and SOR iterative method |
| spellingShingle | Bidhan Chandra Saw Sushanta Man Anupama Bairagi Subhendu Bikash Hazra Gauss-Seidel and Sor Methods for Solving Intuitionistic Fuzzy System of Linear Equations Computer Sciences & Mathematics Forum parametric form of intuitionistic fuzzy number intuitionistic fuzzy linear system (IFLS) Gauss–Seidel and SOR iterative method |
| title | Gauss-Seidel and Sor Methods for Solving Intuitionistic Fuzzy System of Linear Equations |
| title_full | Gauss-Seidel and Sor Methods for Solving Intuitionistic Fuzzy System of Linear Equations |
| title_fullStr | Gauss-Seidel and Sor Methods for Solving Intuitionistic Fuzzy System of Linear Equations |
| title_full_unstemmed | Gauss-Seidel and Sor Methods for Solving Intuitionistic Fuzzy System of Linear Equations |
| title_short | Gauss-Seidel and Sor Methods for Solving Intuitionistic Fuzzy System of Linear Equations |
| title_sort | gauss seidel and sor methods for solving intuitionistic fuzzy system of linear equations |
| topic | parametric form of intuitionistic fuzzy number intuitionistic fuzzy linear system (IFLS) Gauss–Seidel and SOR iterative method |
| url | https://www.mdpi.com/2813-0324/7/1/47 |
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