How to weight Hasse matrices and reduce incomparabilities

This work presents a modified version of Hasse diagram technique, the weighted Regularized Hasse (wR-Hasse), which aims to reduce the number of incomparabilities and derive weighted rankings of the objects. These objectives are accomplished by (a) introducing a mathematical threshold on the definition of incomparability and (b) weighting criteria according to their relevance. In order to test the new approach, we used eight data sets from literature, aiming at extensively investigating the effect of thresholds and weighting schemes on the outcome. Results showed how (a) wR-Hasse effectively reduces the number of incomparabilities with respect to the original Hasse and (b) weighting schemes tune the contribution of relevant criteria to the final outcome. Moreover, this approach allows to obtain statistics useful to further investigate data structure and relationships between object ranks