Spectral CG Algorithm for Solving Fuzzy Non-linear Equations

The non-linear conjugate gradient method is a very effective technique for addressing Large-Scale minimization problems, and it has a wide range of applications in Mathematics, Chemistry, Physics, Engineering, and Medicine, etc. In this paper, we present a new spectral conjugate gradient algorithm, a non-linear conjugate gradient algorithm, whose derivation is based on the Hisham–Khalil (KH) and Newton algorithms Based on Pure Conjugacy Condition, The importance of the research lies in finding an appropriate way to solve all kinds of linear and non-linear fuzzy equations because the Buckley and Qu's method is ineffective in solving all kinds of fuzzy equations and because the conjugate gradient method does not need a Hessian matrix (second partial derivatives of functions) in the solution. The descent property of the suggested method is shown provided that the step size meets the strong Wolfe conditions. In many circumstances, numerical results demonstrate that the novel technique is more efficient than the Fletcher–Reeves (FR) and Hisham–Khalil (KH) procedures in solving Fuzzy Nonlinear Equations.