Interval probability density functions constructed from a generalization of the Moore and Yang integral

TL;DR

This paper generalizes an existing integral concept to define interval probability density functions by allowing intervals as limits and removing monotonicity restrictions, broadening the scope of interval integration.

Contribution

It introduces a new integral framework for interval functions with interval limits, extending previous work and enabling the construction of interval probability density functions.

Findings

New integral definition for interval functions with interval limits

Extension of probability density functions to the interval context

Broader applicability of interval integration methods

Abstract

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.