The (weak) wedgeness for FK-spaces was first defined by Bennett in 1974. Then, some results of Bennett (1974) were improved by İnce (2002) and Da\v{g}adur (2004) for all (weak) wedge FK spaces. In this paper, the concept of wedgeness for an FDK-space $X$ containing $\Phi$ is defined, and some fundamental characterizations related to this space and compactness of the inclusion mapping are studied. Also, some results for a summability domain $X_A^{(\nu)}$ to be (weak) $\nu-$wedge are obtained. Moreover, necessary and sufficient conditions for some double sequence spaces are given.