A generalization of the Moore and Yang integral and interval probability density functions

Based on an extension of Riemann sums, Moore and Yang have defined an integral notion for the context of continuous inclusion monotonic interval functions in which the limits of integration are real numbers. This integral notion generalizes the usual one for real-valued functions based on Riemann sums. In this paper we extend this approach by considering intervals as limits of integration and abolishing the inclusion monotonic restriction of the integrable interval functions. Also, such a new integration notion is used to define interval probability density functions and use it in interval probability distribution functions.

Automated summary

Based on an extension of Riemann sums, this paper introduces a new integral notion that can be applied to continuous inclusion functions with non-monotonic intervals. It further explores the applications of this new integral notion in defining interval probability density functions and interval probability distribution functions.