On Mathematical structures on pairwise comparisons matrices with   coefficients in a group arising from quantum gravity
  We describe the mathematical properties of pairwise comparisons matrices with coefficients in an arbitrary group. We provide a vocabulary adapted for the description of main algebraic properties of inconsistency maps, describe an example where the use of a non abelian group is necessary. Algebraic, topological, geometric and probabilistic aspects are considered. 
Jean-Pierre Magnot
math.GR cs.IT math.IT math.LO