Distributionally robust possibilistic optimization problems - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Fuzzy Sets and Systems Année : 2023

Distributionally robust possibilistic optimization problems

Résumé

In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is used to model imprecise probabilities. In one of interpretation, a possibility distribution (a membership function of a fuzzy set) in the set of coefficient realizations induces a necessity measure, which in turn defines a family of probability distributions in this set. The distributionally robust approach is then used to transform the imprecise constraints into deterministic counterparts. Namely, the uncertain left-hand side of each constraint is replaced with the expected value with respect to the worst probability distribution that can occur. It is shown how to represent the resulting problem by using linear or second-order cone constraints. This leads to problems which are computationally tractable for a wide class of optimization models, in particular for linear programming.

Dates et versions

hal-04071934 , version 1 (17-04-2023)

Identifiants

Citer

Romain Guillaume, Adam Kasperski, Paweł Zieliński. Distributionally robust possibilistic optimization problems. Fuzzy Sets and Systems, 2023, 454 (Special issue: Decision sciences), pp.56-73. ⟨10.1016/j.fss.2022.05.007⟩. ⟨hal-04071934⟩
30 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More