The harmonic consistency index for the analytic hierarchy process

A new consistency measure, the harmonic consistency index, is obtained for any positive reciprocal matrix in the analytic hierarchy process. We show how this index varies with changes in any matrix element. A tight upper bound is provided for this new consistency measure when the entries of matrix a...

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Veröffentlicht in:European journal of operational research 2007-02, Vol.177 (1), p.488-497
Hauptverfasser: Stein, William E., Mizzi, Philip J.
Format: Artikel
Sprache:eng
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Zusammenfassung:A new consistency measure, the harmonic consistency index, is obtained for any positive reciprocal matrix in the analytic hierarchy process. We show how this index varies with changes in any matrix element. A tight upper bound is provided for this new consistency measure when the entries of matrix are at most 9, as is often recommended. Using simulation, the harmonic consistency index is shown to give numerical values similar to the standard consistency index but it is easier to compute and interpret. In addition, new properties of the column sums of reciprocal matrices are obtained.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2005.10.057