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# Properties of fuzzy set spaces with Lp metrics

Submit Time: 2022-06-20
Author: 黄欢 1 ;
Institute: 1.Jimei University;

## Abstracts

 In this paper, we discuss the properties of  the spaces of fuzzy sets in a metric space with $L_p$-type $d_p$ metrics, $p\geq 1$. Firstly, we give the characterizations of compactness in fuzzy set space with $d_p$ metrics. Then we present the completions of fuzzy set spaces with $d_p$ metrics. The $d_p$ metrics are well-defined if and only if a function induced by the Hausdorff metric is measurable. In this paper, we give some fundamental conclusions on the measurability of this function. This paper was submitted to Fuzzy Sets and Systems on 2022.05.06.
From: 黄欢
DOI：10.12074/202110.00083
Recommended references： 黄欢.(2022).具有Lp度量的模糊集空间的性质.[ChinaXiv:202110.00083] (Click&Copy)
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