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1. chinaXiv:202107.00011 [pdf]

Properties of several fuzzy set spaces

Huan Huang
Subjects: Mathematics >> Mathematics (General)

This paper discusses the properties the spaces of fuzzy sets in a metric s- pace equipped with the endograph metric and the sendograph metric, re- spectively. We fist discuss the level characterizations of the Γ-convergence and the endograph metric, and point out the elementary relationships among Γ-convergence, endograph metric and the sendograph metric. On the basis of these results, we present the characterizations of total boundedness, rel- ative compactness and compactness in the space of compact positive α-cuts fuzzy sets equipped with the endograph metric, and in the space of com- pact support fuzzy sets equipped with the sendograph metric, respectively. Furthermore, we give completions of these two kinds of spaces, respectively.

submitted time 2021-11-27 Hits6884Downloads448 Comment 0

2. chinaXiv:202110.00083 [pdf]

Characterizations of compactness in fuzzy set space with Lp metric

黄欢
Subjects: Mathematics >> Mathematics (General)

In this paper, we give characterizations of compactness in fuzzy set space with Lpmetric. Based on these results, we present completions of fuzzy set spaces with Lpmetric. The fuzzy sets discussed in this paper are fuzzy sets in general metric space. We also point out that the results in this paper generalize the results given in our previous paper.

submitted time 2021-10-25 Hits1589Downloads135 Comment 0

3. chinaXiv:202108.00116 [pdf]

Some discussions on Hausdorff metric

黄欢
Subjects: Mathematics >> Mathematics (General)

In this paper, we discuss the properties of functions generated using Hausdorff metric.

submitted time 2021-08-30 Hits2268Downloads256 Comment 0

4. chinaXiv:202108.00057 [pdf]

Properties of fuzzy set

黄欢
Subjects: Mathematics >> Mathematics (General)

In this paper, we give some properties related to platform points of a fuzzy set and their applications.

submitted time 2021-08-10 Hits3598Downloads362 Comment 0

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