不确定序列的依p-阶距离收敛性

发布时间：2018-03-07 15:58

本文选题：不确定变量　切入点：期望　出处：《河北大学》2017年硕士论文　论文类型：学位论文

【摘要】：不确定理论是现实世界中度量不确定程度的一个重要的数学分支.本文分析了不确定理论中关于距离和收敛性的研究成果,指出原有的不确定变量间的距离不满足距离的公理化定义中的三角不等式.因此,在不确定理论的框架下,本文重点讨论了不确定变量间的一类新距离 -阶距离,以及不确定变量序列的收敛性.本文工作进一步丰富了不确定理论的内容,具体研究如下:首先,研究了不确定变量期望的性质,为-阶距离的提出提供了理论依据.其次,提出了不确定变量间的一类新距离 -阶距离,在此基础上给出了不确定变量序列依-阶距离收敛的概念,定义了相应的度量空间并证明了空间的完备性.此外,还提出了不确定向量之间的-阶距离及相应的度量空间并讨论了有关性质.最后,研究了依测度收敛和依-阶距离收敛的一些基本性质,给出了完全收敛的定义,并讨论了依-阶距离收敛和完全收敛与其它收敛性之间的关系.
[Abstract]:Uncertainty theory is an important branch of mathematics to measure the degree of uncertainty in the real world. It is pointed out that the distance between uncertain variables does not satisfy the trigonometric inequality in the axiomatic definition of distance. Therefore, in the framework of uncertainty theory, a new class of distance between uncertain variables is discussed in this paper. And the convergence of uncertain variable sequence. This paper further enriches the content of uncertainty theory. The specific research is as follows: firstly, the properties of uncertain variable expectation are studied, which provides a theoretical basis for putting forward the distance between order and order. In this paper, a new class of distance between uncertain variables is proposed. On the basis of this, the concept of convergence of the sequence of uncertain variables by order distance is given, the corresponding metric space is defined and the completeness of the space is proved. Finally, some basic properties of convergence by measure and distance between uncertain vectors are studied, and the definition of complete convergence is given. The relation between the distance convergence and the complete convergence with other convergence is discussed.
【学位授予单位】：河北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211

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