Abstract
This manuscript presents a novel multi-step, tenth-order iterative method for solving fuzzy nonlinear equations, which frequently emerge in a variety of applications such as optimization, decision-making, control theory, and chemical engineering problems. One of the principal challenges in solving these equations lies in the computational demands of computing and inverting the Jacobian matrix at each iteration. The primary advantage of the proposed iterative method is that it obviates the need for Jacobian matrix calculations, thereby markedly reducing the computational complexity associated with solving fuzzy nonlinear Equations. We conduct a thorough convergence analysis and establish that our method achieves tenth-order convergence. The effectiveness and robustness of the developed approach are illustrated through comprehensive numerical examples and real-life application problems, complete with graphical representations. Furthermore, we compare our method with existing tenth-order iterative methods to demonstrate the superior efficiency of our approach.