Moore and Yang defined an integral notion, based on an extension of Riemann sums, for inclusion monotonic continuous interval functions, where the integrations limits are real numbers. This integral notion extend the usual integration of real functions based on Riemann sums. In this paper, we extend this approach by considering intervals as integration limits instead of real numbers and we abolish the inclusion monotonicity restriction of the interval functions and this notion is used to determine interval probability density functions.

翻译：Moore和Yang根据Riemann总和的延伸,界定了一个整体概念,以包括单声连续间隔功能,其中集成限制为实际数字。这个整体概念扩大了基于Riemann总和的实际功能的通常集成。在本文中,我们通过将间隔作为集成限制而不是实际数字来扩大这一方法,我们取消了对间隔函数的包含单一音量限制,这一概念被用来确定间隔概率密度功能。