On topology of pairwise comparison matrices

Year 2025, Volume: 74 Issue: 2, 346 - 354, 19.06.2025

Selcuk Koyuncu , Ali Mryr Ahamad , Cenap Özel

https://doi.org/10.31801/cfsuasmas.1542622

https://izlik.org/JA44PX58FL

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.

Keywords

Hankel matrix , Lie group , Lie algebra , pairwise comparison matrices

References

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