In this paper, a vector network equilibrium problem with uncertain demands and capacity constraints of arcs is investigated, where the demands belong to a closed interval. By considering two kinds of vector cost functions, i.e., the costs of each path depend on the whole path flow and the path flow itself, the corresponding (weak) vector equilibrium principles are proposed. For the former, some existence results of (weak) vector equilibrium flows are derived based on the vector variational inequalities and the Fan–Browder’s fixed point theorem. For the latter, we introduce the vector minimum cost flow problem with uncertain demands and capacity constraints of arcs. Meanwhile, the relations between the (weak) vector minimum cost flows and the (weak) vector equilibrium flows are revealed. Finally, several numerical examples are given to show the effectiveness of the derived theoretical results.

本文研究了具有不确定需求和电弧容量约束的矢量网络平衡问题，其中需求属于封闭区间。通过考虑两种矢量成本函数，即每条路径的成本取决于整个路径流和路径流本身，提出了相应的（弱）矢量平衡原理。对于前者，基于矢量变分不等式和Fan-Browder不动点定理推导了（弱）矢量平衡流的一些存在结果。对于后者，我们引入了具有不确定需求和电弧容量约束的矢量最小成本流问题。同时，揭示了（弱）向量最小成本流和（弱）向量平衡流之间的关系。最后，