In this paper, we focus on the utilization of the feasible value constraint technique to address multiobjective optimization problems (MOPs). It is attempted to overcome certain drawbacks associated with this method, such as restrictions on functions and weights, inflexibility in constraints, and challenges in assessing proper efficiency. To accomplish this, we propose an improved version of the feasible value constraint technique. Then, by incorporating approximate solutions, we establish connections between $\varepsilon$-(weakly, Properly) efficient points in a general MOP and $\epsilon$-optimal solutions to the scalarization problem.