Knapsack Problem with Uncertain Weights and Values

In this paper, the knapsack problem under uncertain environment is investigated, in which the weights and the values are assumed to be uncertain variables. With different criteria, three mathematical models are constructed for the problem, i.e., expected value model, chance-constrained programming model and uncertain measure model. Taking advantage of uncertainty theory, the first two models can be transformed to their corresponding deterministic forms. We also given a uncertain simulation algorithm to seek the approximate best solution for uncertain measure model. Finally, a numerical example is given to show the applications of the models.