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具有Lp度量的模糊集空间的性质

Properties of fuzzy set spaces with Lp metrics

摘要:In this paper, we discuss the properties ofthe 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 wepresent the completions of fuzzy set spaces with $d_p$ metrics. The $d_p$ metrics are well-definedif and only if a function induced by the Hausdorff metric is measurable.In this paper, we givesome fundamental conclusions on the measurability of this function. This paper was submitted to Fuzzy Sets and Systems on 2022.05.06.

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[V7] 2022-06-20 23:55:29 chinaXiv:202110.00083V7 下载全文
[V6] 2022-06-02 22:23:25 chinaXiv:202110.00083v6 查看此版本 下载全文
[V5] 2022-05-27 23:39:28 chinaXiv:202110.00083v5 查看此版本 下载全文
[V4] 2022-05-07 07:58:04 chinaXiv:202110.00083v4 查看此版本 下载全文
[V3] 2022-04-30 22:07:11 chinaXiv:202110.00083v3 查看此版本 下载全文
[V2] 2022-04-24 21:48:29 chinaXiv:202110.00083v2 查看此版本 下载全文
[V1] 2021-10-25 22:15:52 chinaXiv:202110.00083v1 查看此版本 下载全文
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