A stronger law of large numbers for uncertain random variables

Uncertainty and randomness are two basic types of indeterminacy, which often appears simultaneously in practice. For modelling a complex system with not only uncertainty but also randomness, uncertain random variable is presented to describe the associated parameters and further chance measure is founded. An easy-to-handle case is to consider measurable functions of uncertain variables and random variables. This paper presents a stronger law of large numbers for such a case where random variables are independent but not identically distributed in probability measure and uncertain variables are also independent but not identically distributed in uncertain measure.