Chance-constrained programming with fuzzy stochastic coefficients

Farid Aiche (1) , Moncef Abbas (2) , Didier Dubois (3)

1 UMMTO - Université Mouloud Mammeri [Tizi Ouzou]
2 USTHB - Université des Sciences et de la Technologie Houari Boumediene = University of Sciences and Technology Houari Boumediene [Alger]
3 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage

We consider fuzzy stochastic programming problems with a crisp objective function and linear constraints whose coefficients are fuzzy random variables, in particular of type L-R. To solve this type of problems, we formulate deterministic counterparts of chance-constrained programming with fuzzy stochastic coefficients, by combining constraints on probability of satisfying constraints, as well as their possibility and necessity. We discuss the possible indices for comparing fuzzy quantities by putting together interval orders and statistical preference. We study the convexity of the set of feasible solutions under various assumptions. We also consider the case where fuzzy intervals are viewed as consonant random intervals. The particular cases of type L-R fuzzy Gaussian and discrete random variables are detailed.

Mots clés: Necessity; Possibility; Probability; Convexity; Fuzzy Stochastic Program; Fuzzy Intervals; Random Intervals; Fuzzy Random Variables

Domaines: Intelligence artificielle [cs.AI]; Apprentissage [cs.LG]; Logique en informatique [cs.LO]; Informatique et langage [cs.CL]

Farid Aiche, Moncef Abbas, Didier Dubois. Chance-constrained programming with fuzzy stochastic coefficients. Fuzzy Optimization and Decision Making, 2013, 12 (2), pp.125-152. ⟨10.1007/s10700-012-9151-8⟩. ⟨hal-01121983⟩