Solution of Bipolar Fuzzy Nonlinear Equations by Fuzzy Adomian Decomposition Method and Fuzzy Newton-Raphson Method

Fuzzy nonlinear equations are used to model real-world problems. Due to the nonlinearity, sometimes obtaining a fuzzy solution is challenging. This article deals with two methods for solving such equations, the first is the Fuzzy Newton-Raphson Method and the other is the Fuzzy Adomian Decomposition Method. Both methods are proposed and demonstrated. We observe that the Fuzzy Adomian Decomposition Method (FADM) is better than the Fuzzy Newton-Raphson Method (FNRM). FADM gives a fuzzy solution also, at the core the fuzzy solution matches with the crisp one. The Fuzzy Newton-Raphson Method initially gives a fuzzy solution, but as iterations increase, the solution does not remain fuzzy, and even the fuzzy solution does not match with the crisp one. Lastly, one numerical illustration is solved by both methods.