An Alternative Approach for Solving Dual Fuzzy Nonlinear Equations

Barzilai-Borwein gradient method for solving fuzzy nonlinear equations

“…Thus, where and for , . However, by symmetry in (3) can be written as Hence, we get After solving the fuzzy nonlinear equations and results obtained satisfies the inequality , one can choose the following fuzzy number (4) as the initial guess [3,4,9], and its parametric form is given as ,…”

“…is upper semi-continuous, (2). outside some interval , (3). there are real numbers such that and (3.1)…”

“…However, the convergence is linear and very slow towards the solution point due to lack of gradient information. For more details on numerical methods for solving fuzzy nonlinear equations, please refer to [3,4,12,21]. In this paper, a gradient-base method also known as Barzilai-Borwein gradient method is proposed to solve fuzzy nonlinear equations.…”

Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise?

“…Waziri and Majid proposed a new approach for solving DFN-equations by combining Newton's method for initial iteration and Broyden's method for the rest of the iterations [7]. The paper [8] presents a method of solving DFN-systems based on Chord Newton's method as an improvement of Newton's iterative method published in [5]. An unquestionable advantage of the method [8] is that it requires the Jacobian matrix to be calculated only once for all iterations whereas in Newton's method from [5] the matrix has to be calculated in each subsequent iteration, which is connected with a high computational effort.…”

Solving Dual Fuzzy Nonlinear Equations via Shamanskii Method

“…In [14] suggested a Jacobian updating formula for the Shamanskii method and applied it to solve fuzzy nonlinear equations having singular Jacobian. In [16] employ the Chord's Newton method to solve dual fuzzy nonlinear equations. In [13] further solved dual fuzzy nonlinear problems by Levenberg-Marquardt approach.…”