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

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.

Keywords

• Generalized trapezoidal fuzzy numbers
• Nonlinear equation
• Fuzzified Newton–Raphson method
• Algorithm
• Numerical example