Inconsistency thresholds for incomplete pairwise comparison matrices

Characterization of an inconsistency ranking for pairwise comparison matrices

Pairwise comparisons between alternatives are a well-known method for incorporating preferences of a decision-maker. Since these often do not exhibit consistency, a number of inconsistency indices has been introduced in order to measure the deviation from this ideal case. We axiomatically characterize the inconsistency ranking induced by the Koczkodaj inconsistency index by presenting six indep...

On inconsistency of a pairwise comparison matrix

Improving the Ordinal Inconsistency of Pairwise Comparison Matrices

This paper investigates the effects of non-transitive judgments on the consistency of pairwise comparison matrices and proposes a heuristic algorithm for identifying and eliminating their ordinal inconsistencies. The algorithm is based on graphical representation of the comparison matrices and identifies the edges in the digraph, which are mostly responsible for three-way cycles, representing t...

An LP-based inconsistency monitoring of pairwise comparison matrices

A distance-based inconsistency indicator, defined by the third author for the consistency-driven pairwise comparisons method, is extended to the incomplete case. The corresponding optimization problem is transformed into an equivalent linear programming problem. The results can be applied in the process of filling in the matrix as the decision maker gets automatic feedback. As soon as a serious...

On optimal completions of incomplete pairwise comparison matrices

An important variant of a key problem for multi-attribute decision making is considered. We study the extension of the pairwise comparison matrix to the case when only partial information is available: for some pairs no comparison is given. It is natural to define the inconsistency of a partially filled matrix as the inconsistency of its best, completely filled completion. We study here the uni...