Abstract
Important in pairwise comparisons methods (PC) concepts of reciprocal matrices, consistency conditions and priority vectors of consistent PC matrices are investigated in a more general framework where mappings take values in a not necessarily abelian group. A problem about Pauli's matrices is posed. Notions of left and right priority mappings with respect to a group operation of consistent mappings are introduced. Hou's fixed point theorems on consistent matrices are generalized to theorems on consistent mappings with values in an arbitrarily fixed lattice-ordered group. Relevant to topology basic properties of Koczkodaj's metric which induces Koczkodaj's inconsistency index in PC are studied. It is shown in ZF that Koczkodaj's metric is Cantor complete and not totally bounded, it is equivalent with the Euclidean metric on the set of positive real numbers. A version of Heine–Borel Theorem for Koczkodaj's metric is obtained and briefly applied to the compact bornology of R+n.
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