This paper investigates the dynamic behavior of the novel exponential-type nonlinear fuzzy difference equation motivated by real-world systems with memory-dependent feedback and uncertain parameters. The proposed model: \(\begin{aligned} x_{n+1}=\frac{Cx_n+De^{-x_{n-1}}}{B+Ax_{n-1}},\ n\in N. \end{aligned}\) The model arises naturally in ecological and economic contexts, such as population dynamics with density-dependent inhibition or resource allocation under delayed information. Here, the exponential term \(e^{-x_{n-1}}\) captures saturation effects, initial conditions \(x_{-1},x_0\) and fuzzy coefficients C, D, B, A, are all positive fuzzy numbers, \(\{x_n\}\) denotes the sequence of positive fuzzy numbers, the fuzzy coefficients C, D, B, A reflect uncertainties in system parameters due to incomplete data or environmental fluctuations. We rigorously prove the existence and boundedness of positive solutions, demonstrating that all trajectories remain confined within a compact interval under mild conditions. Furthermore, by combining Lyapunov methods, linearization techniques and monotonicity arguments, we establish the global stability of a unique positive fixed point. The critical role of fuzzy parameters in regulating stability thresholds and convergence rates is highlighted, offering insights for designing robust systems under uncertainty. Our results unify and extend classical stability criteria for nonlinear difference equations, providing a theoretical foundation for applications in biology, economics, and engineering where memory, nonlinearity, and vagueness coexist. Furthermore, we provide several numerical examples to verify the correctness of our conclusions.
