Abstract In this paper, we introduce the notion of $\beta$greedoids and discuss
four basic constructions of $\beta$greedoids namely, deletion,
contraction, direct sum and ordered sum. We show that the operations of deletion
and contraction commute and the direct sum and ordered sum of $\beta$greedoids
$G_{1}$ and $G_{2}$ are interval $\beta$greedoids if and only if
$G_{1}$ and $G_{2}$ are both interval $\beta$greedoids. We also give a
necessary and sufficient condition for the direct sum and ordered sum of
balanced $\beta$greedoids to be balanced.
