The aim of this article is to investigate approximate solutions in an interval-valued multiobjective optimization problem with inequality constraints involving quasidifferentiable functions, which is denoted by QIVMOP. We establish the Karush-Kuhn-Tucker (KKT) type necessary optimality conditions to identify a type-2 \(\mathcal {E}-\) quasi weakly Pareto solution of the QIVMOP under the assumption of a suitable constraint qualification (CQ). We have used the quasidifferential calculus utilizing some results developed in (Antczak in J Optim Theory Appl 171:708–725, 2016). We introduce the concept of approximate convexity and generalized approximate convexity of the functions in terms of quasidifferential sum. We also establish sufficient optimality conditions under the assumptions of generalized approximate convexity of the functions in terms of quasidifferential sum. The concept of approximate version of vector variational inequalities (VVIs) in terms of quasidifferential sum is introduced. Furthermore, we study the relationship between QIVMOP and approximate quasidifferentiable vector variational inequalities ( \(\mathcal {E}-\) QVVIs) under the assumptions of approximate convexity and generalized approximate convexity in terms of quasidifferential sum. We extend some results of (Zhang et al. in Fuzzy Optim Decis Mak 15:33–55, 2016) using quasidifferential analysis. Finally, we apply our results in nonconvex composite interval-valued multiobjtecive optimization models to identify a type-2 \(\mathcal {E}\) -quasi weakly Pareto solution. Several nontrivial numerical examples are furnished to demonstrate the validity of the derived results.
