Recently, Pancaroğlu Akın et al. (2018) defined and studied f-asymptotically $J_{\\delta\\theta}$ -statistical equivalence for sequences of sets. In this paper, firstly, we denote the notions of strongly asymptotically $J_2^{\\delta\\theta}$ -equivalence, f-asymptotically $J_2^{\\delta\\theta}$ -equivalence, strongly f-asymptotically $J_2^{\\delta\\theta}$ -equivalence for double set sequences. Secondly, we investigate some relationships and important properties among these new notions. Then, we denoted asymptotically $J_2^{\\delta\\theta}$ -statistical equivalence for double set sequences. Also, we examine inclusion and necessity relations between them.