Pyramid-Shaped Indicators: Evaluating the Robustness of Scheme Comparisons Under Weight Uncertainty

Abstract

In the digital age, not only has the scope of indicator monitoring expanded but also the indicators themselves have become increasingly multilevel. Theoretically, the greater the number of levels, the more uncertainty there is in the indicators’ weights. This necessitates the evaluation of the robustness of scheme comparisons to reduce evaluation risks. By using partial order evaluation methods as analytical tools, this study aims to delineate the principles and methods of partial order representation for single-level indicators. Based on this delineation, it then aims to analyze the representation methods for multilevel indicators. The results reveal that for a two-level indicator system, it is only necessary to clarify the order of weights between the first- and second-level indicators. Through a partial order Hasse diagram, the schemes can be ranked and the robustness of the comparison can be analyzed. Furthermore, three- and four-level indicator systems can be decomposed into several two-level indicator systems to complete the partial order evaluation. A case analysis demonstrates that the partial order uncertainty analysis method can integrate decision-makers’ preferences. The Hasse diagram not only ranks the schemes but also achieves stratified clustering, which intuitively reflects the stability of the schemes.