  In 2009, Sagan and Savage introduced a combinatorial model for the Fibonomial
numbers, integer numbers that are obtained from the binomial coefficients by
replacing each term by its corresponding Fibonacci number. In this paper, we
present a combinatorial description for the $q$-analog and elliptic analog of
the Fibonomial numbers. This is achieved by introducing some $q$-weights and
elliptic weights to a slight modification of the combinatorial model of Sagan
and Savage.
