A module M is called ?-?ss-supplemented if every submodule X of has a ?ss-supplement Y in which direct summand such that + = and ? Soc? (Y) where Soc?(Y) the sum simple ?-small submodules Y? for some M. Moreover, completely ?-?ss-supplemented. Thus, we present two new types algebraic structures are stronger than ?-D11 ?-D+11-modules, respectively. In this paper investigate basic properties, dec...