Elliptic Generalizations of TOPSIS
[ 1 ] Instytut Informatyki, Wydział Informatyki i Telekomunikacji, Politechnika Poznańska | [ P ] employee
2023
chapter in monograph / paper
english
EN TOPSIS, a popular method for ranking alternatives based on aggregated distances to ideal and anti-ideal points, was considered to be different from widely acknowledged ‘utility-based methods’, which build rankings from weight-averaged utility values. Nonetheless, TOPSIS has recently been shown to be a natural generalization of ‘utility-based methods’ on the grounds that the distances it uses can be decomposed into so-called weight-scaled means (WM) and weight-scaled standard deviations (WSD) of utilities. However, in the standard TOPSIS procedure, the balance that these two components exert on the final ranking cannot be influenced in any way. Building on our previous results, in this paper we put forward modifications that relate TOPSIS aggregations to WM and WSD, achieving well-interpretable control over how the rankings are influenced by WM and WSD. The modifications constitute thus a natural generalization of standard TOPSIS. The generalized TOPSIS may turn into the original TOPSIS or, otherwise, may trade off WM for WSD or WSD for WM. In the latter case, TOPSIS can even be turned into a regular utility-based method. All in all, we believe that the proposed generalizations constitute an interesting practical tool for influencing the ranking by controlled application of a new form of the decision maker’s preferences.
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