According to a generalization of division (g-division) of fuzzy numbers, this paper is concerned with the boundedness, persistence and global behavior of a positive fuzzy solution of the third-order rational fuzzy difference equation
$$x_{n+1}=A+\frac{x_{n}}{x_{n-1}x_{n-2}},\quad n=0,1,\ldots, $$
where A and initial values
$x_{0}$
,
$x_{-1}$
,
$x_{-2}$
are positive fuzzy numbers. Moreover, some examples are given to demonstrate the effectiveness of the results obtained.
