Fuzzy difference equations provide a useful mathematical framework for describing uncertain processes in fields such as engineering, ecology, and the social sciences. Most existing research has been restricted to low-order models, which motivates the present study of a third-order exponential Riccati fuzzy difference equation of the form \(\begin{aligned} x_{n+1} = \frac{\alpha + \beta e^{-x_{n-1}}}{A + x_{n-2}}, \quad \forall \, n \in W, \end{aligned}\) where \(\alpha , \ \beta , \ A\) and the initial conditions \(x_{-2}, \ x_{-1}, \ x_{0}\) are positive fuzzy numbers. By employing the characterization theorem and \(\alpha \) -cut representation, the fuzzy equation is transformed into two crisp systems. The g-division technique is then used to analyze boundedness, persistence, and the local and global stability of equilibrium points. Our results establish the existence and uniqueness of positive solutions, together with sufficient conditions for asymptotic stability. Numerical simulations are included to support and illustrate the theoretical analysis. These findings extend earlier results on second-order models to higher-order fuzzy systems and provide new insights into their qualitative dynamics.
