不确定过程与积分
发布时间：2018-10-09 12:59
【摘要】：自然界中普遍存在着各种各样的不确定现象,基于对这些不确定现象的研究,产生了不确定理论.不确定理论是概率论,可信性理论,信赖性理论的统称,是处理人的信度的数学体系.在不确定理论的框架下,把不确定过程定义为一族随时间变化的不确定变量.基于不确定理论,本文主要对复不确定过程进行了讨论,得出了相关性质,并将不确定微积分推广到复情形,进一步研究了复不确定微积分的性质,给出了不确定无穷积分的定义.为了研究不确定向量,本文还提出了不确定向量的熵.这些结果扩展了不确定理论的研究内容.本文的内容有:1.研究了复不确定过程的一些特性,包括复不确定过程的期望和独立性以及复不确定微积分的性质.2.定义了不确定无穷积分,把不确定过程关于典范过程的积分区间由有限区间推广到了无穷区间.3.提出正则不确定向量的联合分布函数以及不确定向量的熵,为度量不确定向量的不确定性提供了工具.
[Abstract]:There are many kinds of uncertain phenomena in nature. Based on the study of these uncertain phenomena, uncertainty theory is produced. Uncertainty theory is the general term of probability theory, credibility theory and reliability theory, and it is a mathematical system to deal with human reliability. Under the framework of uncertainty theory, the uncertain process is defined as a family of uncertain variables varying with time. Based on the uncertainty theory, this paper mainly discusses the complex uncertain process, obtains the related properties, and extends the uncertain calculus to the complex case, and further studies the properties of the complex uncertain calculus. The definition of indefinite infinite integral is given. In order to study the uncertain vector, the entropy of the uncertain vector is also proposed in this paper. These results extend the research content of uncertainty theory. The content of this article is 1: 1. Some properties of complex uncertain processes are studied, including the expectation and independence of complex uncertain processes and the properties of complex uncertain calculus. The indefinite infinite integral is defined, and the integral interval of uncertain process for canonical process is extended from finite interval to infinite interval. 3. The joint distribution function of the regular uncertain vector and the entropy of the uncertain vector are proposed, which provide a tool for measuring the uncertainty of the uncertain vector.
【学位授予单位】：河北大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O21;O172.2
本文编号：2259421
[Abstract]:There are many kinds of uncertain phenomena in nature. Based on the study of these uncertain phenomena, uncertainty theory is produced. Uncertainty theory is the general term of probability theory, credibility theory and reliability theory, and it is a mathematical system to deal with human reliability. Under the framework of uncertainty theory, the uncertain process is defined as a family of uncertain variables varying with time. Based on the uncertainty theory, this paper mainly discusses the complex uncertain process, obtains the related properties, and extends the uncertain calculus to the complex case, and further studies the properties of the complex uncertain calculus. The definition of indefinite infinite integral is given. In order to study the uncertain vector, the entropy of the uncertain vector is also proposed in this paper. These results extend the research content of uncertainty theory. The content of this article is 1: 1. Some properties of complex uncertain processes are studied, including the expectation and independence of complex uncertain processes and the properties of complex uncertain calculus. The indefinite infinite integral is defined, and the integral interval of uncertain process for canonical process is extended from finite interval to infinite interval. 3. The joint distribution function of the regular uncertain vector and the entropy of the uncertain vector are proposed, which provide a tool for measuring the uncertainty of the uncertain vector.
【学位授予单位】：河北大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O21;O172.2
【相似文献】
相关硕士学位论文 前1条
1 李香谊;不确定过程与积分[D];河北大学;2016年
，本文编号：2259421
本文链接：https://www.wllwen.com/kejilunwen/yysx/2259421.html
