Factor analysis, sparse PCA, and Sum of Ranking Differences-based improvements of the Promethee-GAIA multicriteria decision support technique.

The Promethee-GAIA method is a multicriteria decision support technique that defines the aggregated ranks of multiple criteria and visualizes them based on Principal Component Analysis (PCA). In the case of numerous criteria, the PCA biplot-based visualization do not perceive how a criterion influences the decision problem. The central question is how the Promethee-GAIA-based decision-making process can be improved to gain more interpretable results that reveal more characteristic inner relationships between the criteria. To improve the Promethee-GAIA method, we suggest three techniques that eliminate redundant criteria as well as clearly outline, which criterion belongs to which factor and explore the similarities between criteria. These methods are the following: A) Principal factoring with rotation and communality analysis (P-PFA), B) the integration of Sparse PCA into the Promethee II method (P-sPCA), and C) the Sum of Ranking Differences method (P-SRD). The suggested methods are presented through an I4.0+ dataset that measures the Industry 4.0 readiness of NUTS 2-classified regions. The proposed methods are useful tools for handling multicriteria ranking problems, if the number of criteria is numerous.