12,529 research outputs found
Axiomatization of Inconsistency Indicators for Pairwise Comparisons
This study proposes revised axioms for defining inconsistency indicators in
pairwise comparisons. It is based on the new findings that "PC submatrix cannot
have a worse inconsistency indicator than the PC matrix containing it" and that
there must be a PC submatrix with the same inconsistency as the given PC
matrix.
This study also provides better reasoning for the need of normalization. It
is a revision of axiomatization by Koczkodaj and Szwarc, 2014 which proposed
axioms expressed informally with some deficiencies addressed in this study.Comment: This paper should have been withdrawn by the first author a long time
ago. The work has been finished with another researcher, I have been pushed
out the projec
Pairwise Comparisons Simplified
This study examines the notion of generators of a pairwise comparisons
matrix. Such approach decreases the number of pairwise comparisons from to . An algorithm of reconstructing of the PC matrix from its set
of generators is presented.Comment: 15 pages, two figure
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 error occurs among the matrix elements, even due to a misprint, a significant increase in the inconsistency index is reported. The high inconsistency may be alarmed not only at the end of the process of filling in the matrix but also during the completion process. Numerical examples are also provided
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