Establishing dominance between alternatives with incomplete information in a hierarchically structured attribute tree

A model for establishing dominance with incomplete information is proposed in a hierarchically structured attribute tree. The linear additive value function under certainty is used in the model. The model allows the decision maker to provide any type of linear partial information on the attribute weights and the alternative values. The incompletely specified information constructs a feasible region of linear constraints and therefore, pairwise dominance relationship between alternatives reduces to intractable non-linear programming. Hence, to handle this difficulty, we propose a solution technique. Also, to handle the tree structure, we break down the attribute tree into sub-trees. Due to the recursive structure of the solution technique, the optimization results from sub-trees can be utilized in computing the value interval on the topmost attribute. Based on the solution technique, an algorithm for obtaining the value interval is proposed and dominance relation is established.