随机变量信息度量研究  

Research of Information Measure of Random Variable

作　　者：李武[1] 席酉民[1] 

机构地区：[1]西安交通大学管理学院,西安710049

出　　处：《系统工程理论方法应用》2001年第3期177-179,201,共4页Systems Engineering Theory·Methodology·Applications

基　　金：高等学校博士学科点专项科研基金资助( 980 6 9811) ;国家教育振兴行动计划资助 (A2 19-GL)

摘　　要：指出在决策理论等领域的研究中 ,直接应用 Boltzmann- Shannon熵或其泛化形式来度量随机变量信息时 ,存在 2个缺点 ;随后提出了随机变量信息函数所应满足的 4个条件。在此基础上 ,导出了度量离散随机变量信息的一种新方法 ,并证明了其函数形式的唯一性。这种度量方法保留了信息熵度量的大部分性质 ,并具有一些新的性质。最后将其推广到连续随机变量。将这种信息度量方法应用于决策理论的研究 。It is pointed out that two defects existed in the direct application of Boltzmann Shannon entropy and its general forms to measure random variable information in the research of decision making theory or other fields. Four conditions the random variable information function should satisfy are proposed subsequently, on which, a new method is deduced to measure discrete random variable information and the exclusiveness of its function is demonstrated. This measure retained most properties of Boltzmann Shannon entropy and possessed some new ones. In the end, it is extended to the continuous random variable. Good effects were received when it was put into the research of decision making theory.

关 键 词：信息 随机变量 度量 决策理论 

分 类 号：O236[理学—运筹学与控制论] C934[理学—数学]