Distributionally Robust Optimization in Possibilistic Setting

Romain Guillaume (1) , Adam Kasperski (2) , Pawel Zielinski (2)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 Wroclaw University of Science and Technology

In this paper a class of optimization problems with uncertain constraint coefficients is discussed. Namely, for each ill-known coefficient a possibility distribution, being a membership function of a fuzzy interval, is specified. In a possibilistic interpretation, the induced possibility distribution in the set of constraint coefficient realizations encodes a family of probability distributions in this set. The distributionally robust approach is then used to transform imprecise constraints into crisp counterparts. An extension of the model is proposed, in which individual risk aversion of decision makers is taken into account.

Mots clés: robust optimization; possibility theory; imprecise probabilities; fuzzy intervals

Domaines: Informatique [cs]

Romain Guillaume, Adam Kasperski, Pawel Zielinski. Distributionally Robust Optimization in Possibilistic Setting. International Conference on Fuzzy Systems (FUZZ-IEEE 2021), IEEE, Jul 2021, Luxembourg, Luxembourg. pp.1-6, ⟨10.1109/FUZZ45933.2021.9494390⟩. ⟨hal-03330582⟩