As a generalization of the classes of gwclosed (resp. gwopen, sgwclosed) sets in a weak structure space (X,w), the notions of ij-generalized wclosed (resp. ij-generalized wopen, ij-strongly generalized wclosed) sets in a biweak structure space (X,w1,w2) are introduced. In terms of these concepts, new forms of continuous function between biweak spaces are constructed. Additionally, the concepts of ij-wnormal, ij-gwnormal, ij-wT12, and ij-wσT12 spaces are studied and several characterizations of them are acquired.