  Let $U_{q}^{-}(\mathfrak g)$ be the negative half of a quantum
Borcherds-Bozec algebra $U_{q}(\mathfrak g)$ and $V(\lambda)$ be the
irreducible highest weight module with $\lambda \in P^{+}$. In this paper, we
investigate the structures, properties and their close connections between
three important bases of $U_{q}^{-}(\mathfrak g)$ and $V(\lambda)$; crystal
bases, canonical bases and perfect bases.
  We first re-construct crystal basis theory with modified Kashiwara operators.
While going through Kashiwara's grand-loop argument, we prove several important
lemmas, which play crucial roles in the later developments of the paper.
  Next, based on the theory of canonical bases on quantum Bocherds-Bozec
algebras, we introduce the notion of primitive canonical bases and prove that
primitive canonical bases coincide with lower global bases.
  Finally, we develop the perfect basis theory for quantum Borcherds-Bozec
algebras and prove the existence of lower and upper perfect bases for
$U_{q}^{-}(\mathfrak g)$ and $V(\lambda)$. Moreover, we also prove the
uniqueness of lower and upper perfect crystals. In particular, all the lower
and upper perfect crystals are isomorphic to $B(\infty)$ or $B(\lambda)$.

Representation Theory;Quantum Algebra