A fuzzy difference equation is a difference equation with fuzzy parameters and fuzzy initial values, whose solution is a sequence of fuzzy numbers. They play a key role in the analysis of real-world phenomena, e.g., finance problems, time series, and population models.
The Riccati equation finds various applications in physics and mathematics including random processes, optimal control, and diffusion problems. In this work, we use a generalized division of a fuzzy number to study the existence of a fuzzy difference equation with a positive fuzzy number and the global behaviour of a fuzzy difference equation.