  The extended affine Lie algebra $\widetilde{\frak{sl}_2(\mathbb{C}_q)}$ is
quantized from three different points of view in this paper, which produces
three noncommutative and noncocommutative Hopf algebra structures, and yield
other three quantizations by an isomorphism of
$\widetilde{\frak{sl}_2(\mathbb{C}_q)}$ correspondingly. Moreover, two of these
quantizations can be restricted to the extended affine Lie algebra
${sl_2(\mathbb{C}_q)}$.
