Abstract: In order to determine the distribution of uncertain variables, two central limit theorems for independent and identical variables are proposed. Firstly, the characteristic function of uncertain variables is defined and its calculation formula is given based on the expected value of uncertain variables. Secondly, the properties of the characteristic function are analyzed and the normal distribution in probability theory is introduced into uncertainty theory. It is proved that the distribution can also be regarded as an uncertain one. Finally, an example of shooting accuracy of a new kind of tanks moving at a high speed is given to verify the feasibility and effectiveness of the proposed theorems.

Key words: uncertainty theory; independent and non-identically distributed uncertain variables; central limit theorem; characteristic functions