| Uncertainty occurs when there is more than one realization that can represent an information. This dissertation concerns merely discrete realizations of an uncertainty. Different interpretations of an uncertainty and their relationships are addressed when the uncertainty is not a probability of each realization. A well known model that can handle a linear programming problem with probability uncertainty is an expected recourse model. If uncertainties in the problem have possibility interpretations, an expected average model, which is comparable to an expected recourse model, will be used. These two models can be mixed when we have both probability and possibility uncertainties in the problem, provided these uncertainties do not occur in the same constraint.;This dissertation develops three new solution methods for a linear optimization problem with generalized uncertainty. These solutions are a pessimistic, an optimistic, and a minimax regret solution. The interpretations of uncertainty in a linear programming problem with generalized uncertainty are not limited to probability and possibility. They can be also necessity, plausibility, belief, random set, probability interval, probability on sets, cloud, and interval-valued probability measure. These new approaches can handle more than one interpretation of uncertainty in the same constraint, which has not been done before. Lastly, some examples and realistic application problems are presented to illustrate these new approaches. Some comparisons between these solutions and a solution from the mixed expected average and expected recourse model when uncertainties are probability and possibility are mentioned. |
