Characterization of an inconsistency ranking for 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...

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 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 application of incomplete pairwise comparison matrices for ranking top tennis players

Pairwise comparison is an important tool in multi-attribute decision making. Pairwise comparison matrices (PCM) have been applied for ranking criteria and for scoring alternatives according to a given criterion. Our paper presents a special application of incomplete PCMs: ranking of professional tennis players based on their results against each other. The selected 25 players have been on the t...