Inconsistency indicator maps on groups for pairwise comparisons

This study presents an abelian group approach to analyzing inconsistency in pairwise comparisons. A notion of an inconsistency indicator map on a group, taking values in an abelian linearly ordered group, is introduced. For it, metrics and generalized metrics are utilized. Every inconsistency indicator map generates both a metric on a group and an inconsistency indicator of an arbitrary pairwise comparisons matrix over the group.