This study proposes axioms for inconsistency indicators in pairwise comparisons. The new observation (by Szybowski), that " no PC submatrix may have a worse inconsistency indicator than the given PC matrix " is an essential simplification of the axiomatization. The goal of formulating axioms for all future definitions of new inconsistency indicators is difficult and as illusive as the inconsistency concept itself . This study improves the axiomatization proposed by Koczkodaj and Szwarc in 2014. As a side product, the new axiom allows to prevent approximation error aberrations of an arbitrarily large value in the input data .
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 .
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axioms for
revised axioms for defining
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The new observation (by Szybowski),
It is based on the new findings
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no PC submatrix may
PC submatrix cannot
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given PC matrix
PC matrix containing it
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is an essential simplification of the axiomatization. The goal of formulating axioms for all future definitions of new inconsistency indicators is difficult and as illusive as the inconsistency concept itself
and that there must be a PC submatrix with the same inconsistency as the given PC matrix
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improves the axiomatization proposed
also provides better reasoning for the need of normalization. It is a revision of axiomatization
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in 2014. As a side product, the new axiom allows to prevent approximation error aberrations of an arbitrarily large value in the input data
, 2014 which proposed axioms expressed informally with some deficiencies addressed in this study