  Irredundance has been studied in the context of dominating sets, via the
concept of private neighbor. Here irredundance of zero forcing sets is
introduced via the concept of a private fort and the upper and lower zero
forcing irrdedundance numbers $\mbox{ZIR}(G)$ and $\mbox{zir}(G)$ are defined.
Bounds on $\mbox{ZIR}(G)$ and $\mbox{zir}(G)$ are established and graphs having
extreme values of $\mbox{ZIR}(G)$ and $\mbox{zir}(G)$ are characterized. The
effect of the join and corona operations is studied. As the concept of a zero
forcing irrdedundant set is new, there are many questions for future research.
