We investigated the signed null-additive fuzzy measure $m$, the revised monotone set function which vanishes at the empty set and such that $m(B)=0$ implies $m(A\cup B)=m(A)$ and which is continuous from the above and continuous from below. For such set function $m$, a Jordan decomposition type theorem was proved and this result enabled the definition of the total variation $|m|$ of $m$. The absolute continuity of a null-additive signed fuzzy measure with respect to another null-additive signed fuzzy measure was introduced.