The Combined PSI-ROC Weight Model

The assignment of weights to criteria plays a vital role in addressing multi-objective optimization problems in general and Multi-Criteria Decision-Making (MCDM) problems in particular. This study introduces a new approach for calculating criteria weights, referred to as the Combined PSI-ROC Weight method, and operates in two stages. First, the Preference Selection Index (PSI) method is applied to determine the priority order of the criteria, and then the Rank Order Centroid (ROC) method is used to calculate the weights based on this established order. The effectiveness of the Combined PSI-ROC weight method was tested using two randomly generated numerical examples and one case study involving the evaluation of fire-resistant material criteria. The results indicate that the proposed method outperforms the PSI and Entropy weight methods in maintaining the rank stability of alternatives when assessed by different MCDM techniques. Specifically, the average Spearman correlation coefficients between rankings generated by MCDM methods reached 0.9467, 0.8933, and 0.9444, respectively, when using PSI-ROC weights. In comparison, the PSI method achieved coefficients of 0.8067, 0.8076, and 0.9016, while the Entropy method produced values of 0.9267, 0.7162, and 0.8873.