The Solution of Fully Fuzzy Quadratic Equations Based on Restricted ‎Variation

Document Type : Research Paper


Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, ‎Iran.


Firstly, in this paper, we apply the Fuzzy Restricted Variation Method to achieve an analytical and approximate unsymmetrical fuzzy solution for Fully Fuzzy Quadratic Equation. In this application, after finding the real root of 1-cut of $\tilde{A}\tilde{X}^{2}+\tilde{B}\tilde{X}+\tilde{C}=\tilde{D}$, initial guess is always chosen with possible unknown parameters that leads to highly accurate solution. This technique is applying to solve mentioned equation in four cases via the sign of coefficients and variable that there is not zero in support of them and we solve the problems to find positive or negative solution. This method has been shown to solve effectively, easily and accurately a large class of nonlinear quadratic equations with approximations converging rapidly to accurate solution. In this paper we present the solutions in four cases with formulas, that can be used to write the algorithm for this technique. Finally to illustrate easy application and rich behavior of this method, several examples are ‎given.‎