The purpose of this article is to establish some new results on the Painlevé–Kuratowski convergence of the solution sets for controlled systems of fuzzy vector quasi-optimization problems with a sequence of mappings \(\varGamma _C\)-converging. First, we introduce a new class of controlled systems for fuzzy vector quasi-optimization problems and establish some conditions for the existence of approximate solutions to these problems using the Kakutani–Fan–Glicksberg fixed-point theorem. Then, we study the Painlevé–Kuratowski lower convergence, Painlevé–Kuratowski upper convergence and Painlevé–Kuratowski convergence of the solution sets for such problems. Finally, as a real-world application, we consider the special case of controlled systems of fuzzy traffic network problems. Existence conditions and the Painlevé–Kuratowski convergence of the solution sets for these problems are also investigated and studied. The results presented in the paper are new and extend the main results given by some authors in the literature.

本文的目的是建立具有一系列映射\（\ varGamma _C \）的模糊矢量拟优化问题的控制系统的解集的Painlevé-Kuratowski收敛性的新结果-收敛。首先，我们引入了一类新的模糊矢量准优化问题的控制系统，并使用Kakutani–Fan–Glicksberg不动点定理为这些问题的近似解的存在建立了一些条件。然后，我们研究了针对此类问题的解集的Painlevé-Kuratowski较低收敛性，Painlevé-Kuratowski较高收敛性和Painlevé-Kuratowski收敛性。最后，作为实际应用，我们考虑模糊交通网络问题的受控系统的特殊情况。对这些问题的解集的存在条件和Painlevé-Kuratowski收敛性也进行了研究。本文提供的结果是新的，并且扩展了一些作者在文献中给出的主要结果。