离散型区间概率随机变量和模糊概率随机变量的数学期望  

Mathematical Expectation About Discrete Random Variable With Interval Probability(DRVIP) or Fuzzy Probability(DRVFP)

作　　者：肖盛燮[1] 吕恩琳[2] 

机构地区：[1]重庆交通学院工程力学系,重庆400074 [2]重庆大学工程力学系,重庆400044

出　　处：《应用数学和力学》2005年第10期1253-1260,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(59878057);国家科技攻关计划"西部开发科技行动"重大项目(2004BA901A02)

摘　　要：研究离散型区间概率随机变量和离散型第二类模糊概率随机变量数学期望的性质及求解方法.利用模糊分解定理,把求模糊概率随机变量的数学期望问题化为求一系列区间概率随机变量的数学期望.求区间概率随机变量的数学期望是一个典型的线性规划问题,用单纯形方法推导了求区间概率随机变量数学期望的一个很实用的计算公式.算例表明,用该计算公式得到的结果和用数学规划方法得到的结果完全吻合,但计算过程相对简单.The character and an algorithm about DRVIP（discrete randam variable with interval probability） and the second kind DRVFP （discrete random variable with crisp event-fuzzy probability） are researched. Using the fuzzy resolution theorem, the solving mathematical expectation of a DRVFP can be translated into solving mathematical expectation of a series of RVIP. It is obvious that solving mathematical expectation of a DRVIP is typically solving a linear programming problem. A very functional calculating formula solving mathematical expectation of DRVIP was obtained by using the Dantzig＇s simplex method. The example indicates that the result obtained by using the functional calculate formula fits together completely with the result obtained by using the linear programming method, but the process using the formula deduced is simpler.

关 键 词：区间数 模糊集 概率 随机变量 数学期望 

分 类 号：O159[理学—数学]