  In this work, I consider the logarithmic-corrected and the power-law
corrected versions of the holographic dark energy (HDE) model in the non-flat
FRW universe filled with a viscous Dark Energy (DE) interacting with Dark
Matter (DM). We propose to replace the infra-red cut-off with the inverse of
the Ricci scalar curvature $R$. I obtain the equation of state (EoS) parameter
$\omega_{\Lambda}$, the deceleration parameter $q$ and the evolution of energy
density parameter $\Omega_D'$ in the presence of interaction between DE and DM
for both corrections. I study the correspondence of the logarithmic entropy
corrected Ricci Dark Dnergy (LECRDE) and power-law entropy corrected Ricci Dark
Energy (PLECRDE) models with the the Modified Chaplygin Gas (MCG) and some
scalar fields including tachyon, K-essence, dilaton and quintessence. I also
make comparisons with previous results.
