Implementation of the centroid method of Solymosi and Dombi

Multiple objective decision support, either for selection among finite alternatives or for combining multiple functions in mathematical programming, often involves estimating a set of weights of relative importance. Recently Solymosi and Dombi proposed a means of estimating such weights based upon ordinal preference information. This method relies upon the centroid of bounded weights. Analytic hierarchy process uses ratio estimates of pairwise comparisons. Using only ordinal information, the centroid of weights is developed as an alternative means of weighting hierarchical elements. These weights could be used in selection among alternatives directly, in concordance analysis, or in multiple objective linear programming. Formulation for the centroid of feasible weight values is presented with a table of values for cases where the preference ranking includes no ties. Comparison of the technique on a student job selection decision indicates slight, but insignificant, decline in accuracy relative to the analytic hierarchy based method.