We introduce the definitions of expansivity and topological stability for homeomorphisms on fuzzy metric spaces. We show some basic properties of fuzzy expansive homeomorphisms. Moreover we prove Walters's theorem in the context of fuzzy metric spaces, i.e., a fuzzy expansive system with the fuzzy shadowing property is fuzzy topologically stable.

中文翻译：

---

模糊膨胀图的拓扑稳定性

我们介绍了模糊度量空间上同胚的膨胀性和拓扑稳定性的定义。我们展示了模糊膨胀同胚的一些基本性质。此外，我们在模糊度量空间的上下文中证明了Walters 定理，即具有模糊阴影性质的模糊扩展系统是模糊拓扑稳定的。