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2013 | OriginalPaper | Chapter

2. A New Consistency Test Index for the Data in the AHP/ANP

Authors : Professor Gang Kou, Daji Ergu, Yi Peng, Professor Yong Shi

Published in: Data Processing for the AHP/ANP

Publisher: Springer Berlin Heidelberg

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Abstract

The consistency test is one of the critical components both in AHP and ANP. Currently, the consistency ratio (CR) proposed by Saaty is popularly used to test the consistencies of the pairwise comparison matrices. However, when the number of comparison matrices increases, the consistency test of comparison matrices both in the AHP and ANP becomes complicated. In an attempt to simplify the consistency test, Ergu et al. (2011a) proposed a maximum eigenvalue threshold as the new consistency index for the data in the AHP and ANP, which is mathematically equivalent to the CR method. In addition, a block diagonal matrix is introduced for the comparison matrices in the AHP/ANP to conduct consistency tests simultaneously. In this Chapter, the proposed new consistency test index is comprehensively described.

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previous chapter Introduction
next chapter IBMM for Inconsistent Data Identification and Adjustment in the AHP/ANP
Literature
Barzilai J (1997) Deriving weights from pairwise comparison matrices. J Opl Res Soc 48:1226–1232
Bryson N (1995) A goal programming method for generating priority vectors. J Opl Res Soc 46:641–648
Chu A, Kalaba R, Springam K (1979) A comparison of two methods for determining the weights of belonging to fuzzy sets. J Opt Theory Appl 27:531–541CrossRef
Crawford G, Williams C (1985) A note on the analysis of subjective judgment matrices. J Math Psychol 29:387–405CrossRef
Ergu D, Kou G, Peng Y, Shi Y (2011a) A new consistency index for comparison matrices in the ANP, New State of MCDM in the 21st Century. Lecture notes in economics and mathematical systems, vol 648, part 1, pp 47–56
Ergu D, Kou G, Peng Y, Shi Y, Shi Yu (2011d) The analytic hierarchy process: task scheduling and resource allocation in cloud computing environment. J Supercomput. doi:10.​1007/​s11227-011-0625-1
Saaty TL (1978) Modeling unstructured decision problems-the theory of analytical hierarchies. Math Comput Simulat 20:147–158CrossRef
Saaty TL (1979) Applications of analytical hierarchies. Math Comput Simulat 21:1–20CrossRef
Saaty TL (1980) The analytical hierarchy process. McGraw-Hill, New York
Saaty TL (1990) How to make a decision: the analytic hierarchy process. Eur J Oper Res 48(1):9–26CrossRef
Saaty TL (1991) Some mathematical concepts of the analytic hierarchy process. Behaviormetrika 29:1–9CrossRef
Saaty TL (1994) How to make a decision: the analytic hierarchy process. Interfaces 24:19–43CrossRef
Saaty TL (1996) Decision making with dependence and feedback: the analytic network process. RWS Publications, Pittsburgh. ISBN 0-9620317-9-8
Saaty TL (1999) Fundamentals of the analytic network process. In: ISAHP 1999, Kobe, Japan, 12–14 Aug 1999
Saaty TL (2001a) Decision making with the analytic network process (ANP) and its “super decisions” software: the national missile defense (NMD) example. In: ISAHP 2001 proceedings, Bern, Switzerland, 2–4 Aug 2001
Saaty TL (2001b) Deriving the AHP 1–9 scale from first principles. In: ISAHP 2001 proceedings, Bern, Switzerland
Saaty TL (2003) Decision-making with the AHP: why is the principal eigenvector necessary. Eur J Oper Res 145(1):85–89CrossRef
Saaty TL (2005) Theory and applications of the analytic network process: decision making with benefits, opportunities, costs and risks. RWS Publications, Pittsburgh. ISBN 1-888603-06-2
Saaty TL (2008) The analytic network process. Iran J Oper Res 1(1):1–27
Thurstone L (1927) A law of comparative judgment. Psychol Rev 34(4):273–286CrossRef
Triantaphyllou E, Mann SH (1995) Using the analytic hierarchy process for decision making in engineering applications: Some challenges. Int J Ind Eng Appl Pract 2(1):35–44
Metadata
Title
A New Consistency Test Index for the Data in the AHP/ANP
Authors
Professor Gang Kou
Daji Ergu
Yi Peng
Professor Yong Shi
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Data Processing for the AHP/ANP

Print ISBN: 978-3-642-29212-5

Electronic ISBN: 978-3-642-29213-2

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-29213-2_2