上半连续模糊集空间上Zadeh扩张的拓扑动力学
Topological dynamics of Zadeh's extension on the space of upper semi-continuous fuzzy sets
摘要：
本文给出了具有水平度量的上半连续模糊集空间的不变闭子集上的Zadeh扩张的传递性、轻度混合性、$\mathbf{a}$ -传递性、等度连续性、一致刚性和逼近性的一些刻画。特别地，证明了一个动力系统是弱混合的（分别是，温和混合，弱混合和$\mathbf{a}$ -传递，等度连续，一致刚性）当且仅当Zadeh扩张是传递的（分别，轻度混合、$\mathbf{a}$ -传递、等度连续、均匀刚性）。
英文摘要：
In this paper, some characterizations about transitivity, mildly mixing property, $\mathbf{a}$-transitivity, equicontinuity, uniform rigidity and proximality of Zadeh's extensions restricted on some invariant closed subsets of the space of all upper semi-continuous fuzzy sets with the level-wise metric are obtained. In particular, it is proved that a dynamical system is weakly mixing (resp., mildly mixing, weakly mixing and $\mathbf{a}$-transitive, equicontinuous, uniformly rigid) if and only if the Zadeh's extension is transitive (resp., mildly mixing, $\mathbf{a}$-transitive, equicontinuous, uniformly rigid).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
