<p>This study aims to generalize the concepts of quasi-efficiency and quasi-proper efficiency for variable ordering structures within the framework of vector optimization. In addition to unifying the different concepts of approximate solution defined in the literature, this new concept is useful in problems related to the analysis of non-dominated approximate solutions and minimal approximate solutions. Furthermore, some of the main properties and related theorems are established and, scalarization results and a practical example are presented to demonstrate its efficiency and applicability. Finally, using the new notions of being quasi-non-dominated and quasi-minimal, a generalized subdifferential is defined in vector optimization with variable ordering structures.</p>