On topology of pairwise comparison matrices

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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