This paper introduces a novel approximation technique for solving a specific class of nonsmooth multiobjective interval-valued mathematical problems. We introduce the class of LU- \((\Phi , \rho )\) -invex interval-valued functions, which are connected to the Clarke generalized gradient. Furthermore, we provide significant examples to demonstrate the existence of this class of functions. We show the equivalence between the weakly LU-efficient solution of the considered nonsmooth multiobjective interval-valued mathematical problems and the weakly LU-efficient solution of the associated approximated problem under the proposed invexity assumptions. Additionally, the Mond–Weir dual problems corresponding to the approximated problem are formulated. The duality results for the Mond–Weir dual problems are obtained by applying the duality results previously established for the approximated Mond–Weir and dual problems. The paper also presents numerical examples to illustrate and validate the results.
