In this paper, we derive a sharp condition on the equivalence of topological transitivity among an interval autonomous dynamical system, its induced set-valued system and induced normal fuzzified system. We also prove that their sensitivity (resp., total transitivity) are equivalent. For a general non-autonomous dynamical system, we show the equivalence of topological mixing (resp., mild mixing, cofinite sensitivity, multi-sensitivity and syndetic sensitivity) among the non-autonomous system and its two induced systems. In contrast, we construct a non-autonomous system that is weakly mixing but neither of its two induced systems is weakly mixing. We extend the topological equi-conjugacy between two non-autonomous systems to their two induced systems. Finally, we verify some basic properties of topological entropy among a non-autonomous system and its two induced systems, and establish some sufficient conditions for the topological equi-conjugacy between the fuzzification of a non-autonomous system and a subshift of finite type.

在本文中，我们得出了区间自治动力系统，其诱导集值系统和诱导正态模糊系统之间拓扑传递性等价性的尖锐条件。我们还证明了它们的灵敏度（分别是总传递性）是等效的。对于一般的非自治动力系统，我们显示了非自治系统及其两个诱导系统之间的拓扑混合（等效，轻度混合，有限灵敏度，多重灵敏度和综合灵敏度）的等价性。相反，我们构造了一个弱混合的非自治系统，但是它的两个诱导系统都没有弱混合。我们将两个非自治系统之间的拓扑等共轭扩展到它们的两个诱导系统。最后，