Derivative-free Newton's method for solving intuitionistic fuzzy nonlinear equations with an application

In this paper, we present a derivative-free Newton’s method that avoids computing the derivative by generating an approximation of the derivative for the intuitionistic fuzzy nonlinear equation. We first consider transforming the intuitionistic fuzzy quantities into their equivalent membership and non-membership parametric forms and insert the approximation from the forward difference method applied to F'(x_k) = 0 in Newton’s method to avoid computing the Jacobian matrix. Numerical experiments were carried out, which shows that the approach is a good option for computing Jacobian and is an efficient one.