Evaluating relationship functions in the RANCOM method and their effects on criteria weighting accuracy

This paper investigates the impact of different relationship functions on the performance of the Ranking Comparison (RANCOM) method, a ranking-based approach to calculate criteria weights based on subjective preferences of decision-makers in the Multi-Criteria Decision Analysis (MCDA) field. Three relationship functions (three-value, ratio-based, and logarithmic ratio-based) were evaluated across varying decision contexts using simulated weights generated from Dirichlet distributions with different concentration parameters. The results indicate that no single function performs best in all scenarios. Instead, each excels under specific conditions of weight similarity. The ratio-based function performs best with diverse weights, the logarithmic ratio-based function is superior when weights are similar, and the three-value function remains robust under general conditions. These findings provide valuable guidelines for selecting relationship functions based on expected weight distributions. The study highlights the importance of aligning modeling techniques with decision context and opens avenues for further research into alternative relationship functions and their application in practical decision-making problems.