Multi-attribute decision aid under incomplete information and hierarchical structure

This paper presents methods for dealing with incomplete information about both attribute weights and values under a hierarchically structured value tree. Incomplete information in this paper covers arbitrary linear inequalities and is hence suitable to treat a more general situation than a previous restrictive definition of incomplete information that typically includes interval judgment. This may give decision makers enhanced freedom of choice and ease of specification. We propose two techniques for prioritizing alternatives by (strict) dominance relationship. One is the extension of a previous method for operating flat-structured value trees to hierarchical ones. The other approach propagates pairwise dominance values from leaf nodes to topmost node consecutively which is also an extension of a previous method. Because the strict dominance rule fails to fully prioritize alternatives, as is usually the case under incomplete information, we suggest a new method, a measure of preference strength, which can provide decision makers with a single optimal alternative or full rank of alternatives without any further interaction with decision makers.