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Dergiler / 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
Sayfa
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Yayın Tarihi
2025-06-19
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri:We prove that both additive and multiplicative $PCM$ are connected while only multiplicative consistent $PCM$ is compact.
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Sonuç & Katkı:We also provide that there is no upper bound for the Perron norm of an inconsistent pairwise comparison matrix.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (11)

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  9. Li, C. C., Dong, Y. C., Xu, Y. J., Chiclana, F., Herrera, F., An overview on managing additive consistency of reciprocal preference relations for consistency driven decision making and fusion: taxonomy and future directions, Information Fusion, 52 (2019), 143–156. https://doi.org/10.1016/j.inffus.2018.12.004.
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