中文摘要：

对目标映射和约束映射均为集值映射的向量优化问题（VP）,引入近似Benson真有效解、近似Benson真有效元概念,推广了戎卫东与马毅提出的ε-真有效解,并给出例子予以说明,考虑了集值映射向量优化问题的近似Benson真有效解。在邻近锥次似凸假设条件下,通过数值优化问题的近似解来刻画其近似Benson真有效解,并得到了如下的结论：（x0,y0）是问题（VP）的近似Benson真有效元当且仅当它是对应于问题（VP）的标量化问题（Pμ）的-εσ-C（μ）-次最优元,其必要充分条件具有相同的误差,推广和改进了已有结果。

英文摘要：

In this paper, for vector optimization problems （VP） with the objective function and constraint function are set valued maps, the concepts of approximate Benson properly efficient solutions and approximate Benson properly efficient element are introduced, which extend e-properly efficient solution introduced by Rong Weidong and Ma Yi, and an example is given to illustrate it. Then approximate Benson properly efficient solutions of vector optimization with set-valued maps are considered. Under the assump- tion of nearly cone subconvexlikeness, we obtain the conclusions about the approximate solutions of vector optimization problems through associated scalar optimization problems： （x0, y0 ） is approximate Benson properly efficient element of problem （VP） if and only if it is-εσ-C（μ）-suboptimal element for the scalar problem （Pu） corresponds to （VP）. Especially, the necessary and sufficient conditions have the same error, which extend and improve corresponding ones in the literature.