分类: 数学 >> 数学(综合) 提交时间: 2023-01-14
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 papersignificantly improvethe corresponding conclusions given in our previous paper H. Huang, Characterizations of endograph metric and $ Gamma$-convergence on fuzzy sets, Fuzzy Sets and Systems 350 (2018), 55-84 . The results in this paper are applicable tofuzzy sets in a general metric space. The results in our previous paper are applicable tofuzzy sets in the $m$-dimensional Euclidean space $ mathbb{R}^m$,which is a special type of metric space.Furthermore, based on the above results,wegivethe 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 betweenthe endograph metric and the $ Gamma$-convergence on fuzzy sets.
分类: 数学 >> 数学(综合) 提交时间: 2022-08-13
摘要: This paper shows thatthe endograph metric and the $\Gamma$-convergenceare compatible on a large classof fuzzy set in $\mathbb{R}^m$.
分类: 数学 >> 数学(综合) 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.
分类: 数学 >> 数学(综合) 提交时间: 2022-04-30
摘要: In this paper, we discuss the properties of functions generated using Hausdorff metric.
分类: 数学 >> 数学(综合) 提交时间: 2021-08-10
摘要: In this paper, we give some properties related to platform points of a fuzzy set and their applications.