Modified Barzilai-Borwein (MBB) gradient method for solving fuzzy nonlinear equations

Research has demonstrated that conventional analytical techniques such as the SD, BB, CG, and N approaches are insufficient to solve a collection of fuzzy non-linear equations that involve fuzzy number coefficients[1]. Because of this, the two-step extended gradient method is suggested as an alternative way to resolve these kinds of unclear nonlinear equations. This work uses a six-step technique to solve ambiguous nonlinear equations[7]. This method does not require the Jacobi method and only requires finding a line for t = 0. In order to provide clarification and enhance understanding, two well-known numerical examples are provided to demonstrate the suggested concept, along with their practical results implemented in MATLAB in tables and curves.