On inconsistency of a pairwise comparison matrix

on inconsistency of a pairwise comparison matrix

Determination of weight vector by using a pairwise comparison matrix based on DEA and Shannon entropy

The relation between the analytic hierarchy process (AHP) and data envelopment analysis (DEA) is a topic of interest to researchers in this branch of applied mathematics. In this paper, we propose a linear programming model that generates a weight (priority) vector from a pairwise comparison matrix. In this method, which is referred to as the E-DEAHP method, we consider each row of the pairwise...

On Inconsistency Indices and Inconsistency Axioms in Pairwise Comparisons

Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies focused on the ways how to express and measure this inconsistency, and several inconsistency indices were proposed as an alternative to Saaty’s inconsistency index and inconsistency ratio for reciprocal pairwise comparisons matrices. This paper aim...

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...

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...