Why Hausdorff Distance Is Natural in Interval Computations

Authors

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

Publication Date

8-2016

Comments

Technical Report: UTEP-CS-16-58

Abstract

Several different metrics have been proposed to describe distance between intervals and, more generally, between compact sets. In this paper, we show that from the viewpoint of interval computations, the most adequate distance is the Hausdorff distance d_H(A,A') -- the smallest value ε > 0 for which every element a from the set A is ε-close to some element a' from the ser A', and every element a' from the set A' is ε-close to some element a of the set A.