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MSD-space: Visualizing the inner-workings of TOPSIS aggregations

Author

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  • Susmaga, Robert
  • Szczȩch, Izabela
  • Zielniewicz, Piotr
  • Brzezinski, Dariusz

Abstract

TOPSIS is a popular approach to creating rankings of alternatives characterized by multiple criteria. Over the decades, numerous versions and modifications of the method have been proposed. Nevertheless, the core of TOPSIS, based on calculating and aggregating distances to ideal and anti-ideal alternatives, remains unchanged. This paper aims to describe the inner algebraic aspects of this core, revealing important dependencies between the calculated distances and the mean and standard deviation of the alternative. To visualize the effect of these dependencies on different TOPSIS aggregations, we introduce a new space based on the mean (M) and standard deviation (SD), called MSD-space. MSD-space is a practical tool for comparing aggregations and visualizing the effects that changes to the values of criteria can have on the resulting ratings of alternatives. The advantage of MSD-space is that it can always be successfully illustrated in a plane regardless of the number of criteria describing the alternatives. Using two case studies, we show how MSD-space can help visually compare aggregation functions and formulate improvement actions for selected alternatives. The revealed inner-workings of TOPSIS can be considered a step towards increasing the explainability of TOPSIS itself as well as other multi-criteria ranking methods.

Suggested Citation

  • Susmaga, Robert & Szczȩch, Izabela & Zielniewicz, Piotr & Brzezinski, Dariusz, 2023. "MSD-space: Visualizing the inner-workings of TOPSIS aggregations," European Journal of Operational Research, Elsevier, vol. 308(1), pages 229-242.
    • Handle: RePEc:eee:ejores:v:308:y:2023:i:1:p:229-242
    DOI: 10.1016/j.ejor.2022.12.003
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    References listed on IDEAS

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    1. Kuo, Ting, 2017. "A modified TOPSIS with a different ranking index," European Journal of Operational Research, Elsevier, vol. 260(1), pages 152-160.
    2. Deng-Feng Li, 2009. "Relative Ratio Method For Multiple Attribute Decision Making Problems," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 289-311.
    3. Cinelli, Marco & Kadziński, Miłosz & Miebs, Grzegorz & Gonzalez, Michael & Słowiński, Roman, 2022. "Recommending multiple criteria decision analysis methods with a new taxonomy-based decision support system," European Journal of Operational Research, Elsevier, vol. 302(2), pages 633-651.
    4. Piotr Zielniewicz, 2017. "A Ranking Method Based on the Aggregate Distance Measure Function in the Value Space," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(03), pages 685-710, May.
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    6. Opricovic, Serafim & Tzeng, Gwo-Hshiung, 2004. "Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS," European Journal of Operational Research, Elsevier, vol. 156(2), pages 445-455, July.
    7. Greco, Salvatore & Ishizaka, Alessio & Tasiou, Menelaos & Torrisi, Gianpiero, 2019. "Sigma-Mu efficiency analysis: A methodology for evaluating units through composite indicators," European Journal of Operational Research, Elsevier, vol. 278(3), pages 942-960.
    8. Pengyu Chen, 2019. "A Novel Coordinated TOPSIS Based on Coefficient of Variation," Mathematics, MDPI, vol. 7(7), pages 1-17, July.
    9. Ghaderi, Mohammad & Ruiz, Francisco & Agell, Núria, 2017. "A linear programming approach for learning non-monotonic additive value functions in multiple criteria decision aiding," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1073-1084.
    10. Cinelli, Marco & Kadziński, Miłosz & Gonzalez, Michael & Słowiński, Roman, 2020. "How to support the application of multiple criteria decision analysis? Let us start with a comprehensive taxonomy," Omega, Elsevier, vol. 96(C).
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