Which Classes of Bi-Intervals Are Closed Under Addition?

Authors

Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Jonatan Contreras, The University of Texas at El PasoFollow

Publication Date

6-2020

Comments

Technical Report: UTEP-CS-20-66

Abstract

In many practical situations, uncertainty with which we know each quantity is described by an interval. In processing such data, it is useful to know that the sum of two intervals is always an interval. In some cases, however, the set of all possible value of a quantity is described by a bi-interval -- i.e., by a union of two intervals. It is known that the sum of two bi-intervals is not always a bi-interval. In this paper, we describe all the class of bi-intervals which are closed under addition -- i.e., for which the sum of bi-intervals is a bi-interval.