Expected Value of Function of Uncertain Variables

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