Huan Huang
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 Hits19864, Downloads1155, Comment 0
Huan Huang
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 Hits19862, Downloads1153, Comment 0
马健
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 Hits37697, Downloads4339, Comment 0
黄欢
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. |
黄欢
This paper discusses some properties fuzzy sets. |
Huan Huang
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 Hits19863, Downloads1154, Comment 0
Lai, Chunhui
In 1975, P. Erd\"{o}s proposed the problem of determining the |
Lai, Chunhui
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, $\liminf\sb {n \to \infty} {f(n)-n \over \sqrt n} \geq \sqrt {2 + {2562 \over 6911}}.$ |
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
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. |
Lai, Chunhui
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。 |