Deriving weights from a pairwise comparison matrix over an alo-group

In this paper, at first, we provide some results on the group of vectors with components in a divisible Abelian linearly ordered group, the related subgroup of ⊙ -normal vectors, the relation of ⊙ -proportionality and the corresponding quotient group. Then, we apply the achieved results to the groups of reciprocal and consistent matrices over divisible Abelian linearly ordered groups; this allows us to deal with the problem of deriving a weighted ranking for the alternatives from a pairwise comparison matrix. The proposed weighting vector has several advantages; it satisfies, for instance, the independence of scale-inversion condition.