Numerical solution of fuzzy non-linear equations under generalized trapezoidal fuzziness by Newton–Raphson method
In the real world, we are faced with many problems that cannot be easily described by crisp values, as there is always some uncertainty involved in real-life situations and in those situations, we end up receiving fuzzy values rather than crisp ones in those situations. Some preliminary concepts of...
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Elsevier
2024-12-01
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2773186324000987 |
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| author | Sanjoy Basu G.S. Mahapatra |
| author_facet | Sanjoy Basu G.S. Mahapatra |
| author_sort | Sanjoy Basu |
| collection | DOAJ |
| description | In the real world, we are faced with many problems that cannot be easily described by crisp values, as there is always some uncertainty involved in real-life situations and in those situations, we end up receiving fuzzy values rather than crisp ones in those situations. Some preliminary concepts of fuzzy sets and operations on trapezoidal fuzzy numbers incorporated with the membership function have been discussed here. This paper aims to demonstrate the advantages of the newly developed fuzzified newton–raphson method with the help of trapezoidal fuzzy numbers for solving algebraic nonlinear equations arising in fuzzy environments. The algorithm of newton–raphson techniques for solving the same has been described. This paper presents several examples of how the new fuzzified newton–raphson method works. |
| format | Article |
| id | doaj-art-398baeb5707547a78c13d0cee84fe61f |
| institution | Kabale University |
| issn | 2773-1863 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
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| spelling | doaj-art-398baeb5707547a78c13d0cee84fe61f2024-12-19T11:03:30ZengElsevierFranklin Open2773-18632024-12-019100168Numerical solution of fuzzy non-linear equations under generalized trapezoidal fuzziness by Newton–Raphson methodSanjoy Basu0G.S. Mahapatra1Department of Mathematics, Arignar Anna Government Arts and Science College, Karaikal 609605, Puducherry, India; Department of Mathematics, Dr. Kalaignar M. Karunanidhi Government Institute for Post Graduate Studies & Research, Karaikal 609605, Puducherry, India; Corresponding author at: Department of Mathematics, Arignar Anna Government Arts and Science College, Karaikal 609605, Puducherry, India.Department of Mathematics, National Institute of Technology Puducherry, Karaikal 609609, IndiaIn the real world, we are faced with many problems that cannot be easily described by crisp values, as there is always some uncertainty involved in real-life situations and in those situations, we end up receiving fuzzy values rather than crisp ones in those situations. Some preliminary concepts of fuzzy sets and operations on trapezoidal fuzzy numbers incorporated with the membership function have been discussed here. This paper aims to demonstrate the advantages of the newly developed fuzzified newton–raphson method with the help of trapezoidal fuzzy numbers for solving algebraic nonlinear equations arising in fuzzy environments. The algorithm of newton–raphson techniques for solving the same has been described. This paper presents several examples of how the new fuzzified newton–raphson method works.http://www.sciencedirect.com/science/article/pii/S2773186324000987Generalized trapezoidal fuzzy numbersNonlinear equationFuzzified Newton–Raphson methodAlgorithmNumerical example |
| spellingShingle | Sanjoy Basu G.S. Mahapatra Numerical solution of fuzzy non-linear equations under generalized trapezoidal fuzziness by Newton–Raphson method Franklin Open Generalized trapezoidal fuzzy numbers Nonlinear equation Fuzzified Newton–Raphson method Algorithm Numerical example |
| title | Numerical solution of fuzzy non-linear equations under generalized trapezoidal fuzziness by Newton–Raphson method |
| title_full | Numerical solution of fuzzy non-linear equations under generalized trapezoidal fuzziness by Newton–Raphson method |
| title_fullStr | Numerical solution of fuzzy non-linear equations under generalized trapezoidal fuzziness by Newton–Raphson method |
| title_full_unstemmed | Numerical solution of fuzzy non-linear equations under generalized trapezoidal fuzziness by Newton–Raphson method |
| title_short | Numerical solution of fuzzy non-linear equations under generalized trapezoidal fuzziness by Newton–Raphson method |
| title_sort | numerical solution of fuzzy non linear equations under generalized trapezoidal fuzziness by newton raphson method |
| topic | Generalized trapezoidal fuzzy numbers Nonlinear equation Fuzzified Newton–Raphson method Algorithm Numerical example |
| url | http://www.sciencedirect.com/science/article/pii/S2773186324000987 |
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