Operations Research and Decisions | 2026
Authors: Shih H.-S.; Shyur H.-J.; Hu H.-C.
DOI: 10.37190/ord/217844
Journal: Operations Research and Decisions
Year: 2026
Publisher: Wroclaw University of Science and Technology
Document Type: Article
Open Access: All Open Access; Gold Open Access; Green Open Access
Cited by: 0
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. © 2026 Authors
Dominance; Extreme alternative; Linear normalization; Rank reversal; Relative closeness; TOPSIS