  In this paper, I introduce the concept of $ (\upvarphi, \uppsi) $-finite von
Neumann algebras and I show that if $ \mathscr{M} $ is a finite and $
(\upvarphi, \uppsi) $-finite von Neumann algebra togather with condition $ \{
\big( \Delta(u+v)-\Delta(u)-\Delta(v)\big)^{*}\} \subseteq \uppsi(\mathscr{M})
$, then each (approximately) 2-local $ (\upvarphi, \uppsi) $-derivation $
\delta $ on $ \mathscr{M} $, is a $ (\upvarphi, \uppsi) $-derivation.
