A New Consistency Index for Comparison Matrices in the ANP

Daji Ergu (), Gang Kou (), Yi Peng () and Yong Shi ()
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Daji Ergu: University of Electronic Science and Technology of China
Gang Kou: University of Electronic Science and Technology of China
Yi Peng: University of Electronic Science and Technology of China
Yong Shi: University of Nebraska at Omaha

Chapter Chapter 4 in New State of MCDM in the 21st Century, 2011, pp 47-56 from Springer

Abstract: Abstract The inconsistency test is more difficult in the analytical network process (ANP) than in the analytical hierarchy process (AHP) because there are more comparison matrices in the ANP. The consistency ratio (CR) introduced by Saaty for the AHP is used for inconsistency test in the ANP. When the number of comparison matrices increases, the inconsistency test of comparison matrices in the ANP becomes complicated. In an attempt to simplify the inconsistency test, this paper proposes a maximum eigenvalue threshold as the consistency index for ANP, which is mathematically equivalent to the CR method. In addition, a block diagonal matrix is introduced for the comparison matrices in the ANP to conduct inconsistency tests simultaneously for all comparison matrices. An illustrative example is used to show the effectiveness and the simplicity of the proposed maximum eigenvalue threshold method.

Keywords: Block diagonal matrix; Inconsistency test; Maximum eigenvalue; Maximum eigenvalue threshold; The analytical network process (ANP) (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-642-19695-9_4

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DOI: 10.1007/978-3-642-19695-9_4

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