On homology groups for pairwise comparisons method. (English) Zbl 07897613
Summary: In this study, we introduce pairwise comparisons matrix classification based on homology groups of graphs with unique vertices. Algebraic topology transforms a sequence of topological objects (such as graphs associated with pairwise comparison matrices) into algebraic objects such as homology groups. It is the first attempt to use this tool to classify matrices of pairwise comparisons based on the triads in which the inconsistency occurs. The Koczkodaj inconsistency indicator was used in this study.
Keywords:
inconsistency; first Betti number; homology group; pairwise comparisons method; topological data analysisReferences:
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