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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 74 Issue: 2

On topology of pairwise comparison matrices

Selcuk Koyuncu(University of North Georgia)0000-0001-6720-4751
Ali Mryr Ahamad(University of Jazan)0009-0009-5219-463X
Cenap Özel(King Abdulaziz University)0000-0001-9673-8875
Pages
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Publication Date
2025-06-19
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

We also provide that there is no upper bound for the Perron norm of an inconsistent pairwise comparison matrix.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The aim of this paper is to study the topology of the additive (Lie algebra) and multiplicative (Lie group) pairwise comparison matrices ($PCM$).
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Key Findings & Data:We prove that both additive and multiplicative $PCM$ are connected while only multiplicative consistent $PCM$ is compact.
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Conclusion & Impact:We also provide that there is no upper bound for the Perron norm of an inconsistent pairwise comparison matrix.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hankel matrix · Lie group · Lie algebra

Abstract

The aim of this paper is to study the topology of the additive (Lie algebra) and multiplicative (Lie group) pairwise comparison matrices ($PCM$). We prove that both additive and multiplicative $PCM$ are connected while only multiplicative consistent $PCM$ is compact. We also provide that there is no upper bound for the Perron norm of an inconsistent pairwise comparison matrix.

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Cite This Article

Koyuncu, S., Ahamad, A. M., Özel, C. (2025). On topology of pairwise comparison matrices. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 74 Issue: 2. https://doi.org/10.31801/cfsuasmas.1542622

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