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On distance-based inconsistency reduction algorithms for pairwise comparisons

On distance-based inconsistency reduction algorithms for pairwise comparisons A complete proof of convergence of a certain class of reduction algorithms for distance-based inconsistency (defined in 1993) for pairwise comparisons is presented in this paper. Using pairwise comparisons is a powerful method for synthesizing measurements and subjective assessments. From the mathematical point of view, the pairwise comparisons method generates a matrix (say A) of ratio values (aij) of the ith entity compared with the jth entity according to a given criterion. Entities/criteria can be both quantitative or qualitative allowing this method to deal with complex decisions. However, subjective assessments often involve inconsistency, which is usually undesirable. The assessment can be refined via analysis of inconsistency, leading to reduction of the latter.The proposed method of localizing the inconsistency may conceivably be of relevance for nonclassical logics (e.g., paraconsistent logic) and for uncertainty reasoning since it accommodates inconsistency by treating inconsistent data as still useful information. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Logic Journal of the IGPL Oxford University Press

On distance-based inconsistency reduction algorithms for pairwise comparisons

Koczkodaj, W.W.; Szarek, S. J.
Logic Journal of the IGPL , Volume 18 (6) – Dec 16, 2010
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References (53)

Publisher
Oxford University Press
Copyright
The Author 2010. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org
ISSN
1367-0751
eISSN
1368-9894
DOI
10.1093/jigpal/jzp062
Publisher site
See Article on Publisher Site

Abstract

A complete proof of convergence of a certain class of reduction algorithms for distance-based inconsistency (defined in 1993) for pairwise comparisons is presented in this paper. Using pairwise comparisons is a powerful method for synthesizing measurements and subjective assessments. From the mathematical point of view, the pairwise comparisons method generates a matrix (say A) of ratio values (aij) of the ith entity compared with the jth entity according to a given criterion. Entities/criteria can be both quantitative or qualitative allowing this method to deal with complex decisions. However, subjective assessments often involve inconsistency, which is usually undesirable. The assessment can be refined via analysis of inconsistency, leading to reduction of the latter.The proposed method of localizing the inconsistency may conceivably be of relevance for nonclassical logics (e.g., paraconsistent logic) and for uncertainty reasoning since it accommodates inconsistency by treating inconsistent data as still useful information.

Journal

Logic Journal of the IGPL – Oxford University Press

Published: Dec 16, 2010

Keywords: algorithm convergence pairwise comparisons inconsistency

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