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 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.

Authors

Publication Details

Journal
Franklin Open
Published
2024-10-17
DOI
https://doi.org/10.1016/j.fraope.2024.100168
Citations
4
Primary Topic
Fuzzy Systems and Optimization
Type
article
Field-Weighted Citation Impact
2.84
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article

Numerical solution of fuzzy non-linear equations under generalized trapezoidal fuzziness by Newton–Raphson method

G. S. Mahapatra, Sanjoy Basu
4 citations
Franklin Open
Fuzzy Systems and Optimization
2.84
article

Numerical solution of fuzzy non-linear equations under generalized trapezoidal fuzziness by Newton–Raphson method

G. S. Mahapatra, Sanjoy Basu
article en
4 citations

Abstract

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.

Franklin OpenVol. 9
Openalex Percentile: Top 9%
Fuzzy Systems and Optimization
2.84
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Numerical solution of fuzzy non-linear equations under generalized trapezoidal fuzziness by Newton–Raphson method — G. S. Mahapatra, Sanjoy Basu · Franklin Open (2024) | TGRS Research Map | TGRS