Resolving Rank Reversal in TOPSIS: A Comprehensive Analysis of Distance Metrics and Normalization Methods

Shyur, Huan-Jyh; Shih, Hsu-Shih

doi:10.15388/24-INFOR576

Informatica

Resolving Rank Reversal in TOPSIS: A Comprehensive Analysis of Distance Metrics and Normalization Methods

Huan-Jyh Shyur Hsu-Shih Shih

https://doi.org/10.15388/24-INFOR576

Pub. online: 14 November 2024 Type: Research Article

Open Access

Received
1 June 2024

Accepted
1 October 2024

Published
14 November 2024

Abstract

This paper examines ranking reversal (RR) in Multiple Criteria Decision Making (MCDM) using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). Through a mathematical analysis of min-max and max normalization techniques and distance metrics (Euclidean, Manhattan, and Chebyshev), the study explores their impact on RR, particularly when new, high-performing alternatives are introduced. This research provides insight into the causes of RR, offering a framework that clarifies when and why RR occurs. The findings help decision-makers select appropriate techniques, promoting more consistent and reliable outcomes in real-world MCDM applications.

References

Belton, V., Gear, T. (1983). On a shortcoming of Saaty’s method of analytic hierarchies. Omega, 11, 228–230.

Biswas, A., Gazi, K.H., Sanka, P.M., Ghosh, A. (2024). A decision-making framework for sustainable highway restaurant site selection: AHP-TOPSIS approach based on the fuzzy numbers. Spectrum of Operational Research, 2(1), 1–26.

Cables, E., Lamata, M.T., Verdegay, J.L. (2016). RIM-reference ideal method in multicriteria decision making. Information Sciences, 337-338, 1–10.

Chakraborty, S., Yeh, C.H. (2009). A simulation comparison of normalization procedures for TOPSIS. In: Proceedings of the International Conference on Computers and Industrial Engineering, pp. 1815–1820. https://doi.org/10.1109/ICCIE.2009.5223811.

Chen, P. (2019). Effects of normalization on the entropy-based TOPSIS method. Expert Systems with Applications, 136, 33–41.

Ciardiello, F., Genovese, A. (2023). A comparison between TOPSIS and SAW methods. Annals of Operations Research, 325, 967–994.

Çelen, A. (2014). Comparative analysis of normalization procedures in TOPSIS method: with an application to Turkish Deposit Banking Market. Informatica, 25(2), 185–208. https://doi.org/10.15388/Informatica.2014.10.

de Farias Aires, R.F., Ferreira, L. (2019). A new approach to avoid rank reversal cases in the TOPSIS method. Computers and Industrial Engineering, 132, 84–97.

García-Cascale, M.S., Lamata, M.T. (2012). On rank reversal and TOPSIS method. Mathematical and Computer Modelling, 56, 123–132.

Hwang, C.L., Yoon, K. (1981). Multiple Attribute Decision Making: A State-of-the-Art Survey. Springer-Verlag, Berlin.

İç, Y.T. (2014). A TOPSIS based design of experiment approach to assess company ranking. Applied Mathematics and Computation, 227, 630–647.

Kaliszewski, I., Miroforidis, J., Podkopaev, D. (2018). Multiple criteria decision making and multiobjective optimization – a toolbox. In: Uncertainty and Imprecision in Decision Making and Decision Support: Cross-Fertilization, New Models and Applications: Selected Papers from BOS-2016 and IWIFSGN-2016, Warsaw, Poland, Held on October 12–14, 2016. Springer, pp. 135–142.

Kong, F. (2011). Rank reversal and rank preservation in TOPSIS. Advanced Materials Research, 204-210, 36–41.

Kousar, S., Ansar, A., Kausar, N., Freen, G. (2024). Multi-criteria decision-making for smog mitigation: a comprehensive analysis of health, economic, and ecological impacts. Spectrum of Decision Making and Applications, 2(1), 53–67.

Kulakowski, K., Mazurek, J., Ramík, J., Soltys, M. (2019). When is the condition of order preservation met. European Journal of Operational Research, 277, 248–254.

Kuo, T. (2017). A modified TOPSIS with a different ranking index. European Journal of Operational Research, 260, 152–160.

Li, D.F. (2009). Relative ratio method for multiple attribute decision making problems. International Journal of Information Technology and Decision Making, 8, 289–311.

Mufazzal, S., Muzakkir, S.M. (2018). A new MCDM method based on proximity indexed value for minimizing rank reversals. Computers and Industrial Engineering, 119, 427–438.

Pavličić, D.M. (2001). Normalisation affects the results of MADM methods. Yugoslav Journal of Operations Research, 11(22), 251–265.

Pena, J.C., Nápoles, G., Salgueiro, Y. (2022). Normalization method for quantitative and qualitative attributes in multiple attribute decision-making problems. Expert Systems with Applications, 198, 116821.

Ren, L., Zhang, Y., Wang, Y., Sun, Z. (2007). Comparative analysis of a novel M-TOPSIS method and TOPSIS. Applied Mathematics Research eXpress, 5, 1–10.

Saaty, T.L. (1990a). An exposition on the AHP in reply to the paper “Remarks on the analytic hierarchy process”. Management Science, 36, 259–268.

Saaty, T.L. (1990b). How to make a decision: The analytic hierarchy process. European Journal of Operational Research, 48, 9–26.

Saaty, T.L. (1991). Response to Holder’s comments on the analytic hierarchy process. Journal of the Operational Research Society, 42, 909–914.

Saaty, T.L., Vargas, L.G. (1984). The legitimacy of rank reversal. Omega, 12, 513–516.

Salo, A.A., Hämäläinen, R.P. (1997). On the measurement of preferences in the analytic hierarchy process. Journal of Multi-Criteria Decision Analysis, 6, 309–319.

Senouci, M.A., Mushtaq, M.S., Hoceini, S., Mellouk, A. (2016). TOPSIS-based dynamic approach for mobile network interface selection. Computer Networks, 107, 304–314.

Shen, S. (2021). A Modified TOPSIS Method with Improved Rank Stability and Method Consistency for Multi-criteria Decision Analysis. PhD thesis, George Washington University, Washington, DC.

Shih, H.S., Olson, D.L. (2022). TOPSIS and its Extensions: A Distance-Based MCDM Approach. Springer Nature, Cham, Switzerland.

Tiwari, R.K., Kumar, R. (2021). G-TOPSIS: a cloud service selection framework using Gaussian TOPSIS for rank reversal problem. Journal of Supercomputing, 77, 523–562.

Triantaphyllou, E. (2000). Multi-Criteria Decision Making Methods: A Comparative Study. Kluwer Academic Publishers, Dordrecht/Boston/London.

Triantaphyllou, E. (2001). Two new cases of rank reversals when the AHP and some of its additive variants are used that do not occur with the multiplicative AHP. Journal of Multi-Criteria Decision Analysis, 10(1), 11–25.

von Winterfeldt, D., Edwards, W. (1986). Decision Analysis and Behavioral Research. Cambridge University Press, Cambridge.

Wang, Y.M., Luo, Y. (2009). On rank reversal in decision analysis. Mathematical and Computer Modelling, 49, 1221–1229.

Yang, W. (2020). Ingenious solution for the rank reversal problem of TOPSIS method. Mathematical Problems in Engineering, 9676518.

Yang, W.C., Choe, C.M., Kim, J.S., Om, M.S., Kim, U.H. (2022). Materials selection method using improved TOPSIS without rank reversal based on linear max-min normalization with absolute maximum and minimum values. Materials Research Express, 9, 1–16.

Zanakis, S.H., Solomon, A., Wisharta, N., Dublish, S. (1998). Multi-attribute decision making: a simulation comparison of select methods. European Journal of Operational Research, 107(3), 507–529.

Zavadskas, E.K., Zakarevicius, A., Antucheviciene, J. (2006). Evaluation of ranking accuracy in multi-criteria decisions. Informatica, 17(4), 601–618.

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ranking reversal TOPSIS normalization distance metric extreme alternative

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