Issue: 2026/Vol.36/No.3, Pages 93-109
MANAGING CRITICAL RANK REVERSALS IN TOPSIS: A MATHEMATICAL FRAMEWORK FOR ENSURING STABLE IDEAL SOLUTIONS
Hsu-Shih Shih 
, Huan-Jyh Shyur
, Hung-Ching Hu
Cite as: H. Shih, H. Shyur, H. Hu. Managing critical rank reversals in TOPSIS: A mathematical framework for ensuring stable ideal solutions. Operations Research and Decisions 2026: 36(3), 93-109. DOI 10.37190/ord/217844
Abstract
This research examines the impact of non-dominated alternatives on rankings and explores rank reversal (RR) in the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), a widely used distance-based MCDM method. A theoretical analysis reveals how the mathematical operations of TOPSIS contribute to RR through the relative closeness and separation measures. Four scenarios are outlined to identify conditions where RR becomes unavoidable. The study provides new insights into the mathematical foundations of RR and its implications for decision makers. To address this issue, three strategies are proposed: identifying non-dominated alternatives, recognizing conditions leading to close performance margins, and normalizing ideal solutions to fixed reference values. These findings offer practical guidance for developing distance-based MCDM methods that minimize rank reversal.
Keywords: rank reversal, dominance, relative closeness, linear normalization, extreme alternative, TOPSIS
Received: 20 September 2025 Accepted: 6 February 2026
Published online: 6 February 2026