Advanced Analysis on the Behavior of PROMETHEE Methods under Independence Property and Some Derived Versions

Document Type : Research Paper

Author

University polytechnic of Madrid

Abstract

In this paper, we study the sensitivity of PROMETHEE family methods using four derived versions of Independence property. In particular, we analyse the strangeness of each type of relation (i.e. Indifference, Preference and Incomparability) in the global ranking. On this basis, we establish relevant rules and mathematical conditions upon which PROMETHEE family methods keep their original ranking. In case of change, we propose post-optimality study allowing to expect the new relation between the alternatives while avoiding to process the method. In addition, the intervals of stability of each relation are extracted accordingly. The efficiency of the results is illustrated using numerical examples among what two are real-life cases.  Indeed, the first one describes the project of ranking alternatives for the selection of electric buses in Turkey while the second one defines the problem of scheduling decision making within mechanical workshop for tracks construction in Algeria. Finally, a statistical study comparing the impact of the independence versions using PROMETHEE I, II as well as large number of instances is established.

Keywords


Abbas, M., & Chergui, Z. (2017). Performance of multicriteria decision-making methods: Study and cases. International Journal of Multicriteria Decision Making, 7(2), 116–145.
Abbas, M., & Chergui, Z. (2019). The impact of using a new significant reference point with TOPSIS methods: Study and application. International Journal of Information and Decision Sciences, 11(2), 95–115.
Al-Baldawi, Z. (2024). Assessment lean level in manufacturing enterprises based on fuzzy multi-criteria decision making (FMCDM) - Literature review. International Journal of Supply and Operations Management, 11(1), 1–18.
Arrow, K. J. (1963). Social choice and individual values. Wiley.
Bennadji, K., Seddiki, A., Anouche, M., & Boateng, P. (2016). A multi-criteria group decision-making method for the thermal renovation of masonry buildings: The case of Algeria. Energy and Buildings, 129, 471–483.
Bouyssou, D., Marchant, T., Perny, P., Pirlot, M., Tsoukias, A., & Vincke, P. (2005). Evaluation and decision models with multiple criteria. Hermes - Lavoisier.
Bozóki, S. (2011). Sensitivity analysis in PROMETHEE. Conference Proceedings, IFORS.
Brans, J. P., & Mareschal, B. (2001). PROMETHEE-GAIA: Une méthodologie d’aide à la décision en présence de critères multiples. Éditions de l’Université de Bruxelles.
Chergui, Z., & Jiménez-Martín, A. (2024a). On ordinal information-based weighting methods and comparison analyses. Information, 15(9), 527.
Chergui, Z., & Jiménez-Martín, A. (2024b). An analysis comparing the step-wise weight assessment ratio analysis (SWARA) and the cardinal sum reciprocal (CSR) weighting methods based on simulation techniques. In The 19th ISKE Conference on Intelligence Systems and Knowledge Engineering (FLINS-ISKE 2024). World Scientific Proceedings Series on Computer Engineering and Information Science, Intelligent Management of Data and Information in Decision Making, 211–218.
Chergui, Z., & Jiménez-Martín, A. (2024c). Comparative analysis of two weighting methods accounting for ordinal and additional information: CSR and FUCOM. In 10th International Conference on Control, Decision and Information Technologies (CoDIT 2024), Valetta, Malta, July 1–4. IEEE, 1011–1016. https://doi.org/10.1109/CoDIT.2024.979-8-3503-7397-4
Chergui, Z., & Jiménez-Martín, A. (2024d). On surrogate weighting methods: Some missing comparison analyses. In Proceedings of the International Conference of the African Federation of Operational Research Societies (AFROS). IEEE Press. (In press).
De Smet, Y. (2016). About the computation of robust PROMETHEE II rankings: Empirical evidence. In International Conference on Industrial Engineering and Engineering Management (IEEM) (pp. 1116–1120).
Dejaegere, G., & De Smet, Y. (2022). A new threshold for the detection of possible rank reversal occurrences in PROMETHEE II rankings. International Journal of Multicriteria Decision Making, 9(1), 1–16.
Doan, A. V., & De Smet, Y. (2018). An alternative weight sensitivity analysis for PROMETHEE II rankings. Omega, 80, 166–174.
Genc, T. (2014). Sensitivity analysis on PROMETHEE and TOPSIS weights. International Journal of Management and Decision Making, 13(3), 403–421.
Hamurcu, M., & Eren, T. (2020). Electric bus selection with multicriteria decision analysis for green transportation. Sustainability, 12(7), 2071–1050.
Hwang, C. L., & Yoon, K. (1981). Multiple attribute decision making: Methods and applications. Springer.
Keyser, W. D., & Peeters, P. (1996). A note on the use of PROMETHEE MCDM methods. European Journal of Operational Research, 89(3), 456–461.
Lazim, L., Waimun, A., & Alireza, A. (2018). Application of PROMETHEE method for green supplier selection: A comparative result based on preference functions. Journal of Industrial Engineering International, 15, 271–285.
Mareschal, Y., De Smet, M., & Nemery, P. (2008). Rank reversal in the PROMETHEE II method: Some new results. In International Conference on Industrial Engineering and Engineering Management (pp. 959–963).
Munier, E., Hontoria, N., & Jiménez-Sàez, F. (2019). Strategic approach in multi-criteria decision making. Springer.
Kabassi, K., & Martinis, A. (2021). Sensitivity analysis of PROMETHEE II for the evaluation of environmental websites. Applied Sciences, 11(19), 9215.
Roy, B., & Bouyssou, D. (1993). Aide à la décision multicritère: Méthodes et cas. Economica.
Roy, B., & Figueira, J. R. (2009). A note on the paper: Ranking irregularities when evaluating alternatives by using some ELECTRE methods. Omega, 37(3), 731–733.
Taherdoost, H., & Madanchian, M. (n.d.). Multi-criteria decision making (MCDM) methods and concepts. Encyclopedia, 3.
Vincke, P. (1992). Exploitation of a crisp relation in a ranking problem. Theory and Decision, 32(3), 221–240.
Vahabzadeh, N., & Khamseh, A. (2024). Green ports assessment model regarding uncertainty by best-worst and hesitant fuzzy VIKOR methods: Iranian ports. International Journal of Supply and Operations Management, 11(4), 502–516.
Wang, X., & Triantaphyllou, E. (2006). Ranking irregularities when evaluating alternatives by using some multi-criteria decision analysis methods. In A. Badiru (Ed.), Handbook of Industrial and Systems Engineering (pp. 27–12). CRC Press.
Wolters, W. T. M., & Mareschal, B. (1995). Novel types of sensitivity analysis for additive MCDM methods. European Journal of Operational Research, 81(2), 281–290.
Xianliang, L., & Yunfei, L. (2024). Sensitivity analysis of the parameters for preference functions and rank reversal analysis in the PROMETHEE II method. Omega, 128(1), 103–111.
Zopounidis, M., & Doumpos, C. (2002). Multicriteria classification and sorting methods: A literature review. Journal of Operational Research, 138(2), 229–246.