In the last time important results in multiobjective programming involving type-I functions were obtained (Yuan et al. in: Konnov et al. (eds) Lecture notes in economics and mathematical systems, 2007; Mishra et al. An Univ Bucuresti Ser Mat, LII(2): 207---224, 2003). Following one of these ways, we study optimality conditions and generalized Mond-Weir duality for multiobjective programming involving n-set functions which satisfy appropriate generalized univexity V-type-I conditions. We introduce classes of functions called (ρ, ρ')-V-univex type-I, (ρ, ρ')-quasi V-univex type-I, (ρ, ρ')-pseudo V-univex type-I, (ρ, ρ')-quasi pseudo V-univex type-I, and (ρ, ρ')-pseudo quasi V-univex type-I. Finally, a general frame for constructing functions of these classes is considered.