When is the condition of order preservation met?

This article explores the relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from an alo-group (an Abelian, linearly ordered group) is investigated. This approach allows for a generalization of previous results. Sufficient conditions for order preservation based on the properties of elements of pairwise comparisons matrix are derived. Elucidating numerical examples are presented.