Numerical solution for fuzzy problems by using some descent techniques

The nonlinear conjugate gradient technique is useful for Large-Scale Minimization problems. It has applications in math, chemistry, physics, engineering, medicine, and other fields. Hisham–Khalil (KH) and Newton techniques may be utilized tocreate a nonlinear conjugate gradient algorithm, as outlined in chapter 2. Chapter 3 discusses the spectral conjugate gradient method. Numerical findings reveal that the new strategy outperforms both the Fletcher–Reeves and Khalid–Hisham procedures for solving fuzzy nonlinear equations (FNEs). Chapter 3 introduces a novel spectral conjugate gradient approach whose derivation is based on the Fletcher (CD) and Newton algorithms based on the sole coupling condition, which is proposed in this research and is derived from the Fletcher (CD) algorithm. Numerical data shows that the new technique solves nonlinear fuzzy equations more efficiently than the Fletcher (CD) algorithm. This study is important since Buckley and Qu's technique is inefficient at solving linear and nonlinear fuzzy equations, and the conjugate gradient method does not need a Hessian matrix (second partial derivatives of functions) in the solution. The descent feature of the provided technique meets the strong Wolfe criteria when _k is used as described.