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1. chinaXiv:202107.00011 [pdf]

几个模糊集空间的性质

Huan Huang
Subjects: Mathematics >> Mathematics (General)

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 Γ-convergence, and then investigate the level characterizations?of the endograph metric and the Γ-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 α-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.

submitted time 2022-06-30 Hits19864Downloads1155 Comment 0

2. chinaXiv:202107.00011 [pdf]

几个模糊集空间的性质

Huan Huang
Subjects: Mathematics >> Mathematics (General)

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 Γ-convergence, and then investigate the level characterizations?of the endograph metric and the Γ-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 α-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.

submitted time 2022-06-25 Hits19862Downloads1153 Comment 0

3. chinaXiv:202105.00070 [pdf]

Copula熵:理论和应用

马健
Subjects: Statistics >> Mathematical Statistics
Subjects: Mathematics >> Statistics and Probability
Subjects: Computer Science >> Computer Application Technology
Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science

统计独立性是统计学和机器学习领域的基础性概念,如何表示和度量统计独立性是该领域的基本问题。Copula理论提供了统计相关关系表示的理论工具,而Copula熵理论则给出了度量统计独立性的概念工具。本文综述了Copula熵的理论和应用,概述了其基本概念定义、定理和性质,以及估计方法。介绍了Copula熵研究的最新进展,包括其在统计学的六个基本问题(结构学习、关联发现、变量选择、因果发现、域自适应和正态性检验等)上的理论应用。讨论了前四个理论应用之间的关系,以及其对应的深层次的相关性和因果性概念之间的联系,并将Copula熵的(条件)独立性度量框架与基于核函数和距离相关的同类框架进行了对比。简述了Copula熵在理论物理学、理论化学、化学信息学、水文学、环境气象学、生态学、动物形态学、农学、认知神经学、运动神经学、计算神经学、系统生物学、生物信息学、临床诊断学、老年医学、精神病学、公共卫生学、经济政策学、社会学、政治学,以及能源工程、土木工程、制造工程、可靠性工程、航空航天、通信工程、测绘工程和金融工程等领域的实际应用。

submitted time 2022-06-23 Hits37697Downloads4339 Comment 0

4. chinaXiv:202110.00083 [pdf]

具有Lp度量的模糊集空间的性质

黄欢
Subjects: Mathematics >> Mathematics (General)

In this paper, we discuss the properties of  the 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 we present the completions of fuzzy set spaces with $d_p$ metrics.
The $d_p$ metrics are well-defined if and only if a function induced by the Hausdorff metric is measurable. In this paper, we give some fundamental conclusions on the measurability of this function. This paper was submitted to Fuzzy Sets and Systems on 2022.05.06.

submitted time 2022-06-20 Hits8989Downloads794 Comment 0

5. chinaXiv:202206.00050 [pdf]

模糊集的结果

黄欢
Subjects: Mathematics >> Mathematics (General)

This paper discusses some properties fuzzy sets.

submitted time 2022-06-04 Hits744Downloads234 Comment 0

6. chinaXiv:202107.00011 [pdf]

几个模糊集空间的性质

Huan Huang
Subjects: Mathematics >> Mathematics (General)

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 Γ-convergence, and then investigate the level characterizations?of the endograph metric and the Γ-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 α-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.

submitted time 2022-05-20 Hits19863Downloads1154 Comment 0

7. chinaXiv:202205.00107 [pdf]

关于没有重复循环长度的图的大小

Lai, Chunhui
Subjects: Mathematics >> Discrete Mathematics and Combinatorics

In 1975, P. Erd\"{o}s proposed the problem of determining the
maximum number $f(n)$ of edges in a  graph with $n$ vertices in which
any two cycles are of different
 lengths. In this paper, it is proved that $$f(n)\geq n+\frac{107}{3}t+\frac{7}{3}$$
 for $t=1260r+169 \,\ (r\geq 1)$
 and $n \geq \frac{2119}{4}t^{2}+87978t+\frac{15957}{4}$. Consequently,
$\liminf\sb {n \to \infty} {f(n)-n \over \sqrt n} \geq \sqrt {2 +
\frac{7654}{19071}},$   which is better than the previous bounds
$\sqrt 2$ [Y. Shi, Discrete Math. 71(1988), 57-71], $\sqrt {2.4}$
   [C. Lai,  Australas. J. Combin. 27(2003), 101-105].
   The conjecture $\lim_{n \rightarrow \infty} {f(n)-n\over \sqrt n}=\sqrt {2.4}$ is not true.

submitted time 2022-05-15 Hits721Downloads259 Comment 0

8. chinaXiv:202205.00103 [pdf]

不包含两个相同长度的循环的图形中边数的下限

Lai, Chunhui
Subjects: Mathematics >> Discrete Mathematics and Combinatorics

In 1975, P. Erd\"{o}s proposed the problem of determining the maximum number $f(n)$ of edges in a graph of $n$ vertices in which any two cycles are of different  lengths. In this paper, it is proved that $$f(n)\geq n+32t-1$$ for $t=27720r+169 \,\ (r\geq 1)$  and $n\geq\frac{6911}{16}t^{2}+\frac{514441}{8}t-\frac{3309665}{16}$. Consequently, $\liminf\sb {n \to \infty} {f(n)-n \over \sqrt n} \geq \sqrt {2 + {2562 \over 6911}}.$

submitted time 2022-05-14 Hits2723Downloads294 Comment 0

9. chinaXiv:202205.00042 [pdf]

随机环境下上临界分支过程的非一致性Berry-Esseen估计

范协铨; 吴浩; 叶印娜
Subjects: Mathematics >> Statistics and Probability

设 Zn 是一个独立同分布环境下的上临界分支过程. 本文得到了两个关于 Zn 的非一致性 Berry-Esseen 估计. 该结果把 Grama et al. [Stochastic,Process.,Appl.,127(4),1255-1281,2017] 的 Berry-Esseen 估计推广到了非一致性的情形. 最后, 我们讨论了这些结果在区间估计方面的应用.

submitted time 2022-05-12 Hits2496Downloads308 Comment 0

10. chinaXiv:202205.00033 [pdf]

关于某些图中的边数

Lai, Chunhui
Subjects: Mathematics >> Discrete Mathematics and Combinatorics

设f(n) 是没有等长圈的n个顶点的图的最大可能边数。 确定f(n)的问题由Erdos 在1975 年提出。本文给出了f(n)的下界。

submitted time 2022-05-10 Hits1391Downloads236 Comment 0

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