Distributionally robust possibilistic optimization problems

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