Law of Large Numbers for Uncertain Random Variables

Abstract

The law of large numbers in probability theory states that the average of random variables converges to its expected value in some sense under some conditions. Sometimes, random factors and human uncertainty exist simultaneously in complex systems, and a concept of uncertain random variable has been proposed to study this type of complex systems. This paper aims to provide a law of large numbers for uncertain random variables, which states that the average of uncertain random variables converges in distribution to an uncertain variable. As a byproduct, the convergence of a sequence of uncertain variables is also studied.