Thick Separators

Luc Jaulin (1) , Benoît Desrochers (2)

1 Lab-STICC_ENSTAB_CID_PRASYS
2 DGA Techniques Navales

If an interval of R is an uncertain real number, a thick set is an uncertain subset of Rn. More precisely, a thick set is an interval of the powerset of Rn equipped with the inclusion ⊂ as an order relation. It can generally be defined by parameters or functions which are not known exactly, but are known to belong to some intervals. In this paper, we show how to use constraint propagation methods in order to compute efficiently an inner and an outer approximations of a thick set. The resulting inner/outer contraction are made using an operator which is called a thick separator. Then, we show how thick separators can be combined in order to compute with thick sets.

Domaines: Optimisation et contrôle [math.OC]; Recherche opérationnelle [math.OC]

Luc Jaulin, Benoît Desrochers. Thick Separators. Martine Ceberio; Vladik Kreinovich. Decision Making under Constraints, 276, Springer, pp.125-131, 2020, Studies in Systems, Decision and Control, 978-3-030-40813-8. ⟨10.1007/978-3-030-40814-5_15⟩. ⟨hal-02924180⟩