We develop an alternative approach to Degenerate complex Monge-Amp\`ere
equations on compact K\"ahler manifolds based on the concept of viscosity
solutions and compare systematically viscosity concepts with pluripotential
theoretic ones. We generalize to the K\"ahler case a theorem due to Dinew and
Zhang in the projective case to the effect that their pluripotential solutions
constructed previously by the authors are continuous
