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.

翻译：本文考虑了不确定约束系数下的优化问题。采用可能性理论对不确定性进行建模。具体而言，在约束系数实现（称为场景）上指定了一个联合可能性分布。该可能性分布在场景集上诱导出一种必要性测度，进而描述了场景集中概率分布的一个模糊集。随后采用分布鲁棒方法将不精确约束转化为确定性等价形式。即，通过使用与可能发生的最坏概率分布相关的风险度量来评估不精确约束的左侧。本文采用条件风险值作为风险度量，它推广了文献中常用的严格鲁棒方法和期望值方法。描述了解此类问题的一般框架，并识别出可在多项式时间内求解的特例。