On the Properties of the Priority Deriving Procedure in the Pairwise Comparisons Method
arXiv:1401.8219 · doi:10.3233/FI-2015-1240
Abstract
The pairwise comparisons method is a convenient tool used when the relative order of preferences among different concepts (alternatives) needs to be determined. There are several popular implementations of this method, including the Eigenvector Method, the Least Squares Method, the Chi Squares Method and others. Each of the above methods comes with one or more inconsistency indices that help to decide whether the consistency of input guarantees obtaining a reliable output, thus taking the optimal decision. This article explores the relationship between inconsistency of input and discrepancy of output. A global ranking discrepancy describes to what extent the obtained results correspond to the single expert's assessments. On the basis of the inconsistency and discrepancy indices, two properties of the weight deriving procedure are formulated. These properties are proven for Eigenvector Method and Koczkodaj's Inconsistency Index. Several estimates using Koczkodaj's Inconsistency Index for a principal eigenvalue, Saaty's inconsistency index and the Condition of Order Preservation are also provided.
11 pages
References in corpus (2)
Cited by in corpus (9)
- Inconsistency in the ordinal pairwise comparisons method with and without ties
- Inconsistency indices for incomplete pairwise comparisons matrices
- Towards quantification of incompleteness in the pairwise comparisons method
- On the geometric mean method for incomplete pairwise comparisons
- When is the condition of order preservation met?
- Towards secure judgments aggregation in AHP
- On the similarity between ranking vectors in the pairwise comparison method
- Pairwise Comparisons Matrix Decomposition into Approximation and Orthogonal Component Using Lie Theory
- Manipulation of individual judgments in the quantitative pairwise comparisons method