Grey stochastic multi-criteria decision-making approach based on expected probability degree

After definition of the discrete grey stochastic variable and its expected value, the expected probability degree is defined. For multi-criteria decision-making problems, in which the criteria weights are incompletely certain and the criteria values of alternatives are in the form of grey stochastic variables, a grey stochastic multi-criteria decision-making approach is proposed. In this method, the evaluation value of each alternative under each criterion can be transformed to comprise the expected probability degree judgment matrix, based on which, a non-linear programming model can be enacted. In the end, the genetic algorithm is used to solve the model to attain the criteria weights, and the ranking of alternatives can be produced consequently. The feasibility and validity of this approach are illustrated by an example.