A New Formula for the Moments of Uncertain Variable and Some Applications

In this paper, a method of the generalised inverse of an increasing function is developed. Based on the method of generalised inverse, a new formula for the moments of all uncertain variables is established. By using the new formula, an innovative entropy formula for all uncertain variables is provided in a completely different method. With the entropy formula, the principle of maximum entropy is regained without resorting to the Euler-Lagrange equation. Additionally, two results concerning the expected value of a function for any uncertain variable are provided. In fact, all the results on the regular uncertain variables in uncertainty theory can be extended to all uncertain variables by using the method of generalised inverse.