GBU College Logo
Sign in with GBU Microsoft

Managing Critical Rank Reversals in TOPSIS: A Mathematical Framework for Ensuring Stable Ideal Solutions

Operations Research and Decisions | 2026

Paper Details

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

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. © 2026 Authors

Keywords

Dominance; Extreme alternative; Linear normalization; Rank reversal; Relative closeness; TOPSIS