Expected Value of Function of Uncertain Variables
Expected Value of Function of Uncertain Variables
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发表时间：
2010
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通讯作者：
Yuhan Liu;Minghu Ha
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作者：
Yuhan Liu;Minghu Ha
不确定性理论是建立在正规性、单调性、自对偶性、可数次可加性和乘积度量公理基础上的数学分支。不同于随机性和模糊性，不确定性理论为不确定现象提供了一种新的数学模型。描述不确定量的一个关键概念是不确定变量，期望值算子提供了不确定度量意义下的不确定变量的平均值。本文证明了不确定变量单调函数的期望值就是该函数关于其不确定性分布的勒贝格-斯蒂尔杰斯积分，并给出了一些有用的不确定变量函数期望值的表达式。C
Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. Different from randomness and fuzziness, uncertainty theory provides a new mathematical model for uncertain phenomena. A key concept to describe uncertain quantity is uncertain variable, and expected value operator provides an average value of uncertain variable in the sense of uncertain measure. This paper will prove that the expected value of monotone function of uncertain variable is just a Lebesgue-Stieltjes integral of the function with respect to its uncertainty distribution, and give some useful expressions of expected value of function of uncertain variables. c