  In this paper, an optimization problem with uncertain constraint coefficients
is considered. Possibility theory is used to model the uncertainty. Namely, a
joint possibility distribution in constraint coefficient realizations, called
scenarios, is specified. This possibility distribution induces a necessity
measure in scenario set, which in turn describes an ambiguity set of
probability distributions in scenario set. The distributionally robust approach
is then used to convert the imprecise constraints into deterministic
equivalents. Namely, the left-hand side of an imprecise constraint is evaluated
by using a risk measure with respect to the worst probability distribution that
can occur. In this paper, the Conditional Value at Risk is used as the risk
measure, which generalizes the strict robust and expected value approaches,
commonly used in literature. A general framework for solving such a class of
problems is described. Some cases which can be solved in polynomial time are
identified.
