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arXiv · 1605.06010

Topological dynamics of Zadeh's extension on the space of upper semi-continuous fuzzy sets

Xinxing Wu·Xiong Wang
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Abstract

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).

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Xinxing Wu, Xiong Wang. 2016-05-18. Topological dynamics of Zadeh's extension on the space of upper semi-continuous fuzzy sets. https://doi.org/10.1142/s0218127417501656

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