Existence of extremal solutions for quadratic fuzzy equations

Some results on the existence of solution for certain fuzzy equations are revised and extended. In this paper, we establish the existence of a solution for the fuzzy equation Ex2 + Fx + G = x, where E, F, G, and x are positive fuzzy numbers satisfying certain conditions. To this purpose, we use fixed point theory, applying results such as the well-known fixed point theorem of Tarski, presenting some results regarding the existence of extremal solutions to the above equation.