In this paper, we develop the perfect basis theory for quantum
Borcherds-Bozec algebras Uq​(g) and their irreducible highest
weight modules V(λ). We show that the perfect graph (resp. dual perfect
graph) of every perfect basis (resp. dual perfect basis) of
Uq−​(g) (resp. V(λ)) is isomorphic to B(∞)
(resp. B(λ)). For this purpose, we define a new class of Kashiwara
operators which is different from the one given by Bozec and prove all the
interlocking inductive statements in Kashiwara's grand loop argument, which
shows the existence and the uniqueness of crystal bases for quantum
Borcherds-Bozec algebras