59 research outputs found
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
On Axiomatization of Inconsistency Indicators for Pairwise Comparisons
We examine the notion of inconsistency in pairwise comparisons and propose an
axiomatization which is independent of any method of approximation or the
inconsistency indicator definition (e.g., Analytic Hierarchy Process, AHP). It
has been proven that the eigenvalue-based inconsistency (proposed as a part of
AHP) is incorrect.Comment: Enhanced text, with 21 pages and 3 figures, proves that arbitrarily
inaccurate pairwise matrices are considered acceptable by theories with a
inconsistency based on the principal eigenvalue (e.g., AHP). CPC (corner
pairwise comparisons) matrix is the crucial part of this study as it
invalidates any eigenvalue-based inconsistency. All comments are highly
appreciate
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axioms expressed informally with some deficiencies addressed in this study.Comment: This paper should have been withdrawn by the first author a long time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
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