Laws of large numbers for uncertain variables

So far, little work has been done on laws of large numbers in uncertainty theory. This paper builds two types of laws of large numbers for independent (not necessary identically distributed) uncertain variables on uncertainty space, i.e., Type I law of large numbers and Type II law of large numbers. Note that such two types of laws of large numbers are essentially variants of strong laws of large numbers and weak laws of large numbers on probability space, respectively. Besides, an interesting result is obtained, where convergence almost surely is equivalent to convergence in uncertain measure whenever their relevant universe is finite. All these work not only refines uncertainty theory, but also provides more possibilities for applications of such theories in the future.