Entropy scaling has proved to be an appealing framework to connect transport properties to microscopic structure for many pure fluids. Its extension to mixtures is not fully straightforward in particular because it requires the definition of an effective molecular mass equivalent to that of the mixture from the transport properties point of view. However, the exact definition of such an effective molecular mass, thanks to a mixing rule, is unknown theoretically apart from the zero-density regime. Thus, in this work, various mixing rules that express the effective molecular mass as a function of molar fractions and molecular masses of the components of the mixture, have been investigated by performing molecular simulations on mixtures of Lennard-Jones fluids at various thermodynamic conditions ranging from low- to high-density states. It has been found that the best results are obtained by decomposing the viscosity into zero-density and residual contributions, the latter being described by a correlation based on the entropy scaling.  More precisely, good estimates of the viscosity of mixtures of Lennard-Jones fluids are achieved by using a combination of a van der Waals one fluid-Chapman-Enskog approximation for the zero-density viscosity with a mixing rule derived from the Grunberg-Nissan equation for the residual viscosity. It is even possible to improve these results at high density, using an empirical modification to the Grunberg-Nissan derived mixing rule.