The Combined PSI-ROC Weight Model
Received: 2 September 2025 | Revised: 14 September 2025 | Accepted: 21 September 2025 | Online: 10 October 2025
Corresponding author: Nguyen Trong Mai
Abstract
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.
Keywords:
Multi-Criteria Decision-Making (MCDM), criteria weighting, PSI method, ROC method, combined PSI-ROC method, rank stabilityDownloads
References
M. Bennani, F. Jawab, Y. Hani, A. ElMhamedi, and D. Amegouz, "A Hybrid MCDM for the Location of Urban Distribution Centers under Uncertainty: A Case Study of Casablanca, Morocco," Sustainability, vol. 14, no. 15, Jan. 2022, Art. no. 9544. DOI: https://doi.org/10.3390/su14159544
D. D. Trung, H. T. Dung, N. C. Bao, and D. V. Duc, "A novel approach for determining criteria weights: application in ranking materials for mechanical manufacturing processes," Manufacturing Review, vol. 12, 2025, Art. no. 16. DOI: https://doi.org/10.1051/mfreview/2025014
A. Puška, M. Nedeljković, D. Pamučar, D. Božanić, and V. Simić, "Application of the new simple weight calculation (SIWEC) method in the case study in the sales channels of agricultural products," MethodsX, vol. 13, Dec. 2024, Art. no. 102930. DOI: https://doi.org/10.1016/j.mex.2024.102930
T. V. Dua, D. V. Duc, N. C. Bao, and D. D. Trung, "Integration of objective weighting methods for criteria and MCDM methods: application in material selection," EUREKA: Physics and Engineering, no. 2, pp. 131–148, Mar. 2024. DOI: https://doi.org/10.21303/2461-4262.2024.003171
M. A. Hatefi, "An Improved Rank Order Centroid Method (IROC) for Criteria Weight Estimation: An Application in the Engine/Vehicle Selection Problem," Informatica, vol. 34, no. 2, pp. 249–270, Jan. 2023. DOI: https://doi.org/10.15388/23-INFOR507
N. T. D. Linh, N. H. Son, and D. X. Thao, "Evaluating the Impact of Weighting Methods on the Stability of Scores for Alternatives in Multi-Criteria Decision-Making Problems," Engineering, Technology & Applied Science Research, vol. 15, no. 1, pp. 19998–20004, Feb. 2025. DOI: https://doi.org/10.48084/etasr.9518
M. Alemi-Ardakani, A. S. Milani, S. Yannacopoulos, and G. Shokouhi, "On the effect of subjective, objective and combinative weighting in multiple criteria decision making: A case study on impact optimization of composites," Expert Systems with Applications, vol. 46, pp. 426–438, Mar. 2016. DOI: https://doi.org/10.1016/j.eswa.2015.11.003
B. Németh et al., "Comparison of weighting methods used in multicriteria decision analysis frameworks in healthcare with focus on low- and middle-income countries," Journal of Comparative Effectiveness Research, vol. 8, no. 4, pp. 195–204, Mar. 2019, https://doi.org/10.2217/cer-2018-0102. DOI: https://doi.org/10.2217/cer-2018-0102
S. Zakeri, D. Konstantas, P. Chatterjee, and E. K. Zavadskas, "Soft cluster-rectangle method for eliciting criteria weights in multi-criteria decision-making," Scientific Reports, vol. 15, no. 1, Jan. 2025, Art. no. 284. DOI: https://doi.org/10.1038/s41598-024-81027-4
R. N. Wardany and Zahedi, "A study comparative of PSI, PSI-TOPSIS, and PSI-MABAC methods in analyzing the financial performance of state-owned enterprises companies listed on the Indonesia stock exchange," Yugoslav Journal of Operations Research, vol. 35, no. 2, pp. 313–330, 2025. DOI: https://doi.org/10.2298/YJOR240115017W
T. V. Dua, "Development of the PSI-RAPS-MCRAT method: a hybrid model," EUREKA: Physics and Engineering, no. 1, pp. 141–151, 2025. DOI: https://doi.org/10.21303/2461-4262.2025.003404
A. R. Paramanik, S. Sarkar, and B. Sarkar, "OSWMI: An objective-subjective weighted method for minimizing inconsistency in multi-criteria decision making," Computers & Industrial Engineering, vol. 169, Jul. 2022, Art. no. 108138. DOI: https://doi.org/10.1016/j.cie.2022.108138
P. Valentinas, Z. Edmundas Kazimieras, and P. Askoldas, "An Extension of the New Objective Weight Assessment Methods CILOS and IDOCRIW to Fuzzy MCDM," Economic Computation and Economic Cybernetics Studies and Research, vol. 54, no. 2, pp. 59–75, Jun. 2020. DOI: https://doi.org/10.24818/18423264/54.2.20.04
T. Varshney et al., "Investigation of rank order centroid method for optimal generation control," Scientific Reports, vol. 14, no. 1, May 2024, Art. no. 11267. DOI: https://doi.org/10.1038/s41598-024-61945-z
K. Maniya and M. G. Bhatt, "A selection of material using a novel type decision-making method: Preference selection index method," Materials & Design, vol. 31, no. 4, pp. 1785–1789, Apr. 2010. DOI: https://doi.org/10.1016/j.matdes.2009.11.020
X. T. Hoang, "Multi-Objective Optimization of Turning Process by Fuca Method," Strojnícky časopis - Journal of Mechanical Engineering, vol. 73, no. 1, pp. 55–66, May 2023. DOI: https://doi.org/10.2478/scjme-2023-0005
B. Kizielewicz and A. Bączkiewicz, "Comparison of Fuzzy TOPSIS, Fuzzy VIKOR, Fuzzy WASPAS and Fuzzy MMOORA methods in the housing selection problem," Procedia Computer Science, vol. 192, pp. 4578–4591, Jan. 2021. DOI: https://doi.org/10.1016/j.procs.2021.09.236
P. Aazagreyir, P. Appiahene, O. Appiah, and S. Boateng, "Comparative Analysis of Fuzzy Multi-criteria Decision-making Methods for Quality of Service-based Web Service Selection." Social Science Research Network, Rochester, NY, 2023. DOI: https://doi.org/10.11591/ijai.v13.i2.pp1408-1419
D. D. Trung, "Using RAM method for optimal selection of flame retardant nanocomposite material fabrication solution," EPJ Applied Metamaterials, vol. 11, 2024, Art. no. 4. DOI: https://doi.org/10.1051/epjam/2024005
Downloads
How to Cite
License
Copyright (c) 2025 Nguyen Hoai Son, Duong Van Duc, Nguyen Trong Mai
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.
