Avoiding Fake Boundaries in Set Interval Computing

Authors

Anthony Welte, École Nationale Supérieure de Techniques Avancées BretagneFollow
Luc Jaulin, École Nationale Supérieure de Techniques Avancées BretagneFollow
Martine Ceberio, 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-16-56

Abstract

Set intervals techniques are an efficient way of dealing with uncertainty in spatial localization problems. In these techniques, the desired set (e.g., set of possible locations) is represented by an expression that uses intersection, union, and complement of input sets -- which are usually only known with interval uncertainty. To find the desired set, we can, in principle, perform the corresponding set-interval computations one-by-one. However, the estimates obtained by such straightforward computations often contain extra elements -- e.g., fake boundaries. In this paper, we show that we can eliminate these fake boundaries (and other extra elements) if we first transform the original set expression into an appropriate DNF/CNF form.