Yes it can be understood as a quantization procedure. You are probably familiar with the first step to giving a quantization is to give a Poisson algebra. In this case you want the algebra in question to be better than the coordinate ring of the group, you want it to be the coordinate ring of a Poisson-Lie group.

Let's focus on the identity. Now I'm giving you a Lie bialgebra. Many examples come from looking at QR or LU factorizations. Here you see Etingof-Kazhdan.

I recommend Semenov-Tian-Shansky's lecture notes http://arxiv.org/pdf/q-alg/9703023.pdf

Yes it can be understood as a quantization procedure. You are probably familiar with the first step to giving a quantization is to give a Poisson algebra. In this case you want the algebra in question to be better than the coordinate ring of the group, you want it to be the coordinate ring of a Poisson-Lie group.

Let's focus on the identity. Now I'm giving you a Lie bialgebra. Many examples come from looking at QR or LU factorizations. Here you see Etingof-Kazhdan.

I recommend Semenov-Tian-Shansky's lecture notes http://arxiv.org/pdf/q-alg/9703023.pdf

Edit: the deformation parameter has a different interpretation not necessarily $\hbar$, so be careful when you have multiple deformations.