Imprecise information in multi-level decision trees

Sammanfattning: The information available to decision makers is often vague and imprecise, and various methods based on interval estimates of probabilities and utilities have been proposed to deal with this. The discussion has, however, mostly evolved around representation, and much less has been done to take into consideration the evaluation, and also computational and implementation aspects has been left out. The Delta method for handling vague and imprecise information is one of the most elaborated approaches in its category and is therefore a reasonable starting point for this thesis. However, one major disadvantage is that the approach only handles single-level decision trees and cannot nontrivially be extended to handle multi-level trees. The capability of handling multi-level trees is important, since it appears naturally in many real-life situations. The purpose of this thesis is to present a generalization allowing for multi-level trees and imprecise information, thus extending the Delta approach. The extension is implemented in the decision software DecideIT, which consequently allows for interval statements and value comparisons between different consequences, in the form of multi-level trees. Five papers are attached to the thesis. Two of these present the necessary algorithms and an implementation employing them. The third and fourth papers demonstrate how decision problems can be modelled and evaluated taking into account the imprecise input data. A fifth paper presents how the method can be extended to a multi-attribute decision tree evaluation method.