分类: 数学 >> 数学(综合) 提交时间: 2022-06-30
摘要: This paper discusses the properties the spaces of fuzzy sets in a metric space?equipped with the endograph metric and the sendograph metric, respectively.?We fist give some relations among the endograph metric, the sendograph?metric and the -convergence, and then investigate the level characterizations?of the endograph metric and the -convergence. By using the above results,?we give some relations among the endograph metric, the sendograph metric,?the supremum metric and the dp* metric. On the basis of the above results,?we present the characterizations of total boundedness, relative compactness?and compactness in the space of compact positive -cuts fuzzy sets equipped?with the endograph metric, and in the space of compact support fuzzy sets?equipped with the sendograph metric, respectively. Furthermore, we give?completions of these metric spaces, respectively.
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.