Distributionally Robust Optimization in Possibilistic Setting

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.

Automated summary

This paper discusses a class of optimization problems with uncertain constraint coefficients using possibility distributions to encode a family of probability distributions. The distributionally robust approach is applied to transform imprecise constraints into crisp counterparts, with an extension of the model taking into account individual risk aversion of decision makers.