Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric mean method for judgement matrices: Formulas for errors   The geometric mean method (GMM) and the eigenvector method (EM) are
well-known approaches to deriving information from pairwise comparison matrices
in decision making processes. However, the original algorithms of these methods
are logically incomplete and have significant drawbacks: their actual numerical
errors are unknown and their reliability is doubted by different rank reversal
phenomena including the GMM-EM ones.
  Recently (Tomashevskii 2015: Eur J Oper Res 240:774-780), the actual
numerical errors were found for EM, and it was shown that all EM rank reversal
phenomena have the same cause and are eliminated when the errors are taken into
account. In this paper the similar ap-proach is used for GMM: we associate GMM
with some standard measuring procedure, ana-lyze this procedure from the
viewpoint of measurement theory, and find the actual GMM errors. We show that
the GMM and the GMM-EM rank reversal phenomena are eliminated when the GMM and
the EM errors are taken into account.
  The GMM decision support tool, which has all components of a standard
measuring tool, is composed of pairwise comparisons as an initial measuring
procedure, GMM as a data processor, and the obtained formulas for GMM errors as
an error indicator. This tool is analogous to the EM decision support tool
received earlier in the above paper. It is shown that the EM and the GMM
versions of the tool are equally suitable to measure and rank any comparable
elements with positive numerical values.
  We also analyze the Geometric Consistency Index usually used in the original
GMM to measure of the inconsistency and to accept or reject an inconsistent
pairwise comparison matrix, and show that this index is not an acceptable GMM
error indicator.

31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
1
The categories of this paper are: cs
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
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The categories of this paper are: q-fin
7
The categories of this paper are: hep-th