带endograph度量的模糊集空间的紧性刻画
Characterizations of compactness of fuzzy set space with endograph metric
AI总结：
该研究给出了带endograph度量的一般度量空间模糊集空间的全有界性、相对紧性与紧性刻画，改进了此前仅适用于欧氏空间的结论，还拓展至常见子空间并探究了其与Γ-收敛的关联。
摘要：
本文提出了配备endograph（上图）度量的模糊集空间中全有界性、相对紧性与紧性的刻画结论。本文所得结论显著改进了我们此前论文[H. Huang, Characterizations of endograph metric and $Γ$-convergence on fuzzy sets, Fuzzy Sets and Systems 350 (2018), 55-84]中的对应结果。本文结论适用于一般度量空间中的模糊集，而我们此前论文的结论仅适用于$m$维欧氏空间$\bbR^m$中的模糊集——这是度量空间的一种特例。此外，基于上述结果，我们还给出了一般模糊集的一类常见子空间在endograph度量下的相对紧性、全有界性与紧性刻画。作为应用，本文探究了模糊集上endograph度量与$Γ$-收敛之间的若干关联。
英文摘要：
In this paper, we present the characterizations of total boundedness, relative compactness and compactness in fuzzy set spaces equipped with the endograph metric. The conclusions in this paper significantly improve the corresponding conclusions given in our previous paper [H. Huang, Characterizations of endograph metric and $Γ$-convergence on fuzzy sets, Fuzzy Sets and Systems 350 (2018), 55-84]. The results in this paper are applicable to fuzzy sets in a general metric space. The results in our previous paper are applicable to fuzzy sets in the $m$-dimensional Euclidean space $\mathbb{R}^m$, which is a special type of metric space. Furthermore, based on the above results, we give the characterizations of relative compactness, total boundedness and compactness in a kind of common subspaces of general fuzzy sets according to the endograph metric. As an application, we investigate some relationship between the endograph metric and the $Γ$-convergence on fuzzy sets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
