  A. Ishii and K. Oshiro introduced the notion of an $f$-twisted Alexander
matrix. This notion is a quandle version of the twisted Alexander matrix which
was introduced by M. Wada. They showed that the twisted Alexander matrix of a
pair of a link group and a group representation can be recovered from the
$f$-twisted Alexander matrix of a pair of a link quandle and a quandle
homomorphism. In this paper, we study a relationship between the $f$-twisted
Alexander matrix and the quandle cocycle invariant. As an application, we show
that an $f$-twisted Alexander invariant of knot quandles is a really stronger
oriented knot invariant than a twisted Alexander invariant of knot groups.
