When is the condition of order preservation met?

TL;DR

This paper investigates the conditions under which order preservation holds in pairwise comparisons matrices with elements from an alo-group, generalizing previous results and providing sufficient conditions for order consistency.

Contribution

It introduces a generalized framework for pairwise comparisons matrices using alo-groups and derives new sufficient conditions for order preservation.

Findings

Derived sufficient conditions for order preservation.

Generalized pairwise comparisons matrices using alo-groups.

Presented a numerical example illustrating the results.

Abstract

This article explores a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from an alo-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. A numerical example is presented.