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Tools for establishing dominance with linear partial information and attribute hierarchy

The multiple attribute decision-making problem is dealt with when a decision-maker incompletely articulates their preferences about the attribute weight and alternative value. Furthermore, the attribute tree, which is structured hierarchically, is considered. Techniques for establishing dominance with linear partial information are proposed in a hierarchically structured attribute tree. The linear additive value function under certainty is used in the model. The incompletely specified information constructs a feasible region of linear constraints and therefore the pairwise dominance relationship between alternatives leads to intractable non-linear programming. Hence, solution techniques are proposed to handle this difficulty. Also, to handle the tree structure, the attribute tree is break down into subtrees. Due to the recursive structure of the solution technique, the optimization results from subtrees can be used in computing the interval on the topmost attribute. The intervals computed by the proposed solution techniques can be used to establish the pairwise dominance relation between alternatives. The pairwise dominance relation will be represented as strict dominance and weak dominance, which have already been defined in previous research.