具有Lp度量的模糊集空间的性质

• 作者： 黄欢 ¹
• 作者单位：
  1.  Jimei University
• 提交时间：2022-06-20

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.

• 来自： 黄欢
• 分类： 数学 >> 数学（综合）
• 引用： ChinaXiv:202110.00083 (或此版本 ChinaXiv:202110.00083V7)
  doi:10.12074/202110.00083
  CSTR:32003.36.ChinaXiv.202110.00083.V1
• 推荐引用方式： 黄欢.(2022).具有Lp度量的模糊集空间的性质.CSTR:32003.36.ChinaXiv.202110.00083.V7 (点此复制)