Depending on the amount of data to process, file generation may take longer.

If it takes too long to generate, you can limit the data by, for example, reducing the range of years.


Download BibTeX


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


[ 1 ] Instytut Informatyki, Wydział Informatyki i Telekomunikacji, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.3] Information and communication technology

Year of publication


Published in

European Journal of Operational Research

Journal year: 2023 | Journal volume: vol. 308 | Journal number: no. 1

Article type

scientific article

Publication language


  • Multi-criteria decision analysis
  • Multi-criteria ranking
  • Aggregated distance ranking
  • Visualization

EN 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.

Date of online publication


Pages (from - to)

229 - 242




Ministry points / journal


Impact Factor

6,4 [List 2022]

This website uses cookies to remember the authenticated session of the user. For more information, read about Cookies and Privacy Policy.