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Avoiding Fake Boundaries in Set Interval Computing

Anthony Welte Luc Jaulin 1, 2 Martine Ceberio 3 Vladik Kreinovich 3
1 Lab-STICC_ENSTAB_CID_PRASYS
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
2 Pôle STIC_OSM
ENSTA Bretagne - École Nationale Supérieure de Techniques Avancées Bretagne
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. It was known 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. In this paper, we prove a new result, that any DNF/CNF form enables us to eliminate the extra elements – thus, we can use the shortest possible DNF/CNF form and therefore, speed up the corresponding computations.
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https://hal-ensta-bretagne.archives-ouvertes.fr/hal-01698416
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Dernière modification le : mercredi 5 août 2020 - 03:50:38
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  • HAL Id : hal-01698416, version 1

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Anthony Welte, Luc Jaulin, Martine Ceberio, Vladik Kreinovich. Avoiding Fake Boundaries in Set Interval Computing. Journal of Uncertain Systems, World Academic Press, 2017, 11 (2), pp.137 - 148. ⟨hal-01698416⟩

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