Spectral Fletcher (CD) Algorithm for Solving Fuzzy Non-Linear Equations

Abstract

A conjugate gradient method is a powerful tool for solving large-scale miniaturization issues, with applications in arithmetic, chemistry, physics, engineering, medicine, and other fields. In this paper, we introduce a new spectral conjugate gradient algorithm, whose derivation is based on the Fletcher (CD) and Newton algorithms based on the solely coupling condition, which is introduced in this study. The significance of the research is in identifying a suitable algorithm. Because the Buckley and Qu methods are ineffectual in solving all types of ambiguous equations, and the conjugate gradient approach does not require a Hessian matrix (second partial derivatives of functions) in the solution, it is used to solve all types of ambiguous equations. The suggested method's descent property is demonstrated as long as the α_kstep size matches the strong Wolfe conditions. In many cases, numerical findings demonstrate that the novel technique is more efficient in solving nonlinear fuzzy equations than Fletcher (CD) algorithm.