On the differentiability of interval functions

TL;DR

This paper examines the inaccuracies in previous characterizations of the derivatives of interval functions and provides corrections to improve understanding of their differentiability.

Contribution

It identifies errors in prior work on interval function derivatives and offers a corrected characterization of when these derivatives exist.

Findings

Previous characterizations of interval derivatives are inaccurate.

The paper provides corrected conditions for the existence of derivatives.

Clarifies the mathematical understanding of interval function differentiability.

Abstract

Two articles published by Information Science discuss the derivatives of interval functions, in the sense of Svetoslav Markov. The authors of these articles tried to characterize for which functions and points such derivatives exist. Unfortunately, their characterization is inaccurate. This article describes this inaccuracy and explains how it can be corrected.