We describe the algebraic properties of pairwise comparisons matrices with coefficients in an arbitrary group. We provide a vocabulary adapted for the description of main algebaric properties of inconsistency maps, describe an example where the use of a non abelian group is necessary, and decribe a generalization of pairwise comparisons matrices and inconsistency maps on a graph.

introduction: solubility of mineral trioxide aggregate (mta) is an important characteristic that affects other properties such as microleakage and biocompatibility. distilled water (dw) has previously been used for solubility tests. this experimental study compared the solubility of mta in dw, synthetic tissue fluid (stf) and new simulated plasma (sp). methods and materials: in this study, 36 s...

The Consistency Index and the Ratio of analytic hierarchy process (AHP) were designed to measure ratio inconsistent judgments among pairwise comparisons (PCs), which have been principal indices for past four decades. Definitions inconsistency measures PCs yet be established, however, because difficulty in quantifying subjectivity judgments. Therefore, an empirical review that can take such subj...