Inner approximations of coherent lower probabilities and their application to decision making problems
针对概率信息不精确的决策问题，提出将初始概率模型转化为具有更好数学性质的子类模型（如超模性或完全单调性），通过线性或二次规划求解，并应用于严重不确定性下的决策。
Abstract We consider a decision making problem under imprecision, where the probabilistic information is given in terms of a set of probability measures, and where finding the optimal alternative(s) may be difficult. To ease the computation, we propose to transform the initial model into another one that (1) belongs to some subclass with better mathematical properties, such as supermodularity or complete monotonicity; (2) is at least as informative as the original model, while being as close as possible to it. We show that the problem can be approached in terms of linear or quadratic programming and that it can be connected with the one of determining the incenter of a credal set. Finally, we compare the solutions of a decision making problem with the initial and the transformed models and illustrate how our approach can be applied in a decision making problem under severe uncertainty.