Liu [7] proposed uncertain calculus, where the integrand is defined on closed interval. Is it integrable on infinite interval? In order to solve this problem, a kind of general uncertain integral is defined in this paper. However, to calculate general uncertain integral according to the definition is very difficult. Thus, some properties and theorems of this kind of general uncertain integral are obtained in this paper, which will be helpful to judge the convergence and calculate general uncertain integral.

uncertain variable, uncertain process, uncertain integral, general uncertain integral.