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本文将函数序列的ｖ－收敛性（ｖａｒｉａｔｉｏｎａｌｃｏｎｖｅｒｇｅｎｃｅ）推广到向量值函数，在ｖ－收敛性的条件下得到了给定的多目标决策问题的近似弱有效解集的下半连续性并给出了若干容易验证的充分条件．在一致收敛性和不变凸性（ｉｎｖｅｘｉｔｙ）的条件下得到了近似有效解集的连续性．作为本文一般性结果的应用，得到了求解多目标ｍｉｎｉｍａｘ（最小最大）问题的一种有效的逼近方法：极大熵方法的收敛性质．
In this paper, the variationalconvergence of a function sequence is generalized to a vector-valued function, and the lower semicontinuity of the approximate weakly efficient solution set for a given multi-objective decision-making problem is given under the condition of v-convergence. A number of easy to verify the sufficient conditions. The continuity of the approximate effective solution set is obtained under the condition of uniform convergence and invexity. As an application of the general result in this paper, an efficient approximation method for solving the multi-objective minimax problem is obtained: the convergence property of the maximum entropy method.