Approximate problems that scalarize and approximate a given multiobjective
optimization problem (MOP) became an important and interesting area of
research, given that, in general, are simpler and have weaker existence
requirements than the original problem. Recently, necessary conditions for
approximation of several types of efficiency for MOPs have been obtained
through the use of an alternative theorem. In this paper, we use these
results in order to extend them to sufficient conditions for approximate quasi
(weak, proper) efficiency. For this, we use two scalarization techniques of
Tchebycheff type. All the provided results are established without convexity
assumptions.