Optimization under uncertainty using possibility and necessity distributions consistent with probability distributions

A standard formulation of a constrained optimization problem is examined where it is assumed that several parameters of the functions involved are uncertain. It is assumed that each such parameter can be represented by a probability distribution and the problem restated as a stochastic programming problem. This research examines the reformulation of the stochastic programming problem when the uncertain parameters are replaced with possibility and necessity distributions that are consistent with the probability distributions. It is shown that the reformulated problem optimizes an estimate of the expected value of the original problem.