In this paper, the connectedness of solution sets for generalized vector equilibrium problems via free-disposal sets (GVEPVF) in complete metric space is discussed. Firstly, by virtue of Gerstewitz scalarization functions and oriented distance functions, a new scalarization function \(\omega \) is constructed and some properties of it are given. Secondly, with the help of \(\omega \), the existence of solutions for scalarization problems (GVEPVF)\(_\omega \) and the relationship between the solution sets of (GVEPVF)\(_\omega \) and (GVEPVF) are obtained. Then, under some suitable assumptions, sufficient conditions of (path) connectedness of solution sets for (GVEPVF) are established. Finally, as an application, the connectedness results of E-efficient solution set for a class of vector programming problems are derived. The obtained results are new, and some examples are given to illustrate the main results.

本文讨论了在完整度量空间中通过自由处置集（GVEPVF）求解广义矢量均衡问题的解集的连通性。首先，利用Gerstewitz标量函数和定向距离函数，构造了一个新的标量函数\（\ omega \）并给出了其一些性质。其次，借助\（\ omega \），存在标量问题（GVEPVF）\（_ \ omega \）的解以及（GVEPVF）\（_ \ omega \）的解集之间的关系和（GVEPVF）被获得。然后，在一些适当的假设下，建立了（GVEPVF）的解集的（路径）连通性的充分条件。最后，作为一种应用，推导了针对一类向量规划问题的E-有效解集的连通性结果。获得的结果是新的，并提供了一些示例以说明主要结果。