A hierarchical interactive method for ranking alternatives with multiple qualitative criteria

Abstract

In this study we deal with the problem of finding the most preferred composite ranking of a set of alternatives evaluated using a large number of criteria having a hierarchical structure. The criteria may be qualitative or quantitative. The decision maker evaluates alternatives using each criterion at the lowest (basic) level. That information is then used to construct the generalized correlation matrix to describe interdependencies between the criteria. The correlation matrix and the criterion hierarchy are the basic information used in the approach. Our interactive approach is designed to help the decision maker find the most preferred aggregation of the kth level criteria, which produces the criteria at the ( k + 1)st level. As the final result of the aggregation we obtain the strength of the preference matrix for the criterion at the highest level. By means of that matrix, we produce the final ranking of the alternatives using the Bowman and Colantoni (1973) model. The approach is easy to implement and convenient to use. We have implemented an experimental version of it on an Apple III microcomputer. The graphical colour display is used as an aid in finding the most preferred aggregation. An illustrative example is provided.