This paper concerns a kind of fuzzy third-order nonlinear difference equation $$ x_{n+1}=A+Bx_n+\frac{x_n}{x_{n-1}x_{n-2}},\ \ n=0,1,\cdots,$$from the Bobwhite quail population model, where the parameters $A,B$ and initial values $x_i (i=-2,-1,0)$ are positive parabolic fuzzy numbers. According to g-division of fuzzy sets and based on the symmetrical parabolic fuzzy numbers, the conditional stability of this model is proved, besides the existence, boundedness and persistence of its unique positive fuzzy solution. Then, the relative Allee effect analysis is done by contrasting the Zadeh extension principle with g-division. The extinction thresholds with fuzzy degree is illustrated. As a Supplement, several numerical examples and table are interspersed to illustrate the effectiveness.
MSC: 39A10