Comparing Subjective Weighting Methods in Multi-Criteria Decision-Making: An Application to Electric Bicycle Ranking

Ranking the various electric bicycle models available in the market, each with different specifications, is a complex task. The importance of criteria in this process depends on subjective weighting methodsbecause the assigned weights to the criteria are based on the decision-maker's subjective priorities. This study compares three subjective weighting methods, namely the Rank Order Centroid (ROC) method, the Rank Sum (RS) method, and a method based on the Lagrange multiplier (referred to as the Lagrange method). These methods share the common characteristic of deriving weights from the evaluation of criteria, yet they differ in their specific formulas. The three methods were applied to assign weights to the criteria used in evaluating seven electric bicycle models across 10 different criteria. The weights were calculated under 10 different scenarios, each reflecting a change in the prioritization of criteria. For each scenario, four Multi-Criteria Decision-Making (MCDM) methods were used to rank the electric bicycles: Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Ranking of Alternatives with Weights of Criterion (RAWEC), Particle Image Velocimetry (PIV), and Root Assessment Method (RAM). The comparison of weighting methods was based on the average Spearman rank correlation coefficient between the MCDM rankings obtained using different weighting methods. The findings indicate that the ROC and Lagrange methods outperformed the RS method.