Comparison of Multi-Criteria Decision Analysis methods under comprehensive sensitivity analysis

In many contemporary decision-making environments, practitioners must navigate complex problems characterized by multiple, conflicting criteria. Multi-Criteria Decision Analysis (MCDA) methods have become essential tools for structuring such evaluations, enabling more transparent and data-driven recommendations. However, their practical usefulness depends on both their theoretical foundations and their ability to perform reliably under uncertain or changing input data. Despite their widespread integration into Decision Support Systems (DSS), there remains a lack of systematic investigation into how robust different MCDA methods are when exposed to variability in the decision data. This study addresses this gap by investigating the stability and sensitivity of four selected used MCDA methods, Root Assessment Method (RAM), Complex Proportional Assessment (COPRAS), Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS), and Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS). These methods were chosen based on their diverse computational assumptions and approaches to preference calculation, providing a representative basis for comparing stability across different methodological principles. The analysis employs the Comprehensive Sensitivity Analysis Method (COMSAM), a systematic framework that introduces simultaneous perturbations into the decision matrix to simulate real-world uncertainty. Through both simulation experiments and a practical facility location problem, the study reveals significant differences in method stability. RAM demonstrated the highest robustness, maintaining consistent preference rankings, while TOPSIS was most sensitive to matrix fluctuations. The findings highlight the critical role of method selection in DSS design, particularly in dynamic environments. The study contributes a structured comparative framework and empirical benchmarks that support the development of reliable MCDA-based decision tools under conditions of uncertainty.