PRIORITY EIGENVECTORS IN ANALYTIC HIERARCHY/NETWORK PROCESSES WITH OUTER DEPENDENCE BETWEEN ALTERNATIVES AND CRITERIA
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Abstract
This work continues consideration of the relations between Analytic Hierarchy and Network processes. It shows that in the case of a simple network with outer dependence between alternatives and criteria, the priority vectors can be constructed not only via the powered supermatrix but also by the eigenvectors of the supermatrix. The relationship to the AHP least squares approach and other methods of priority estimation are considered as well. An ANP matrix of local eigenvectors includes priorities for all the compared items in the whole network. Here we interpret the complex AHP/ANP connections and show clearly how they result in priority estimations useful for applied decision making.
http://dx.doi.org/10.13033/ijahp.v3i2.123
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AHP, ANP, outerdepence, supermatrix, eigenvectors
rank. Psycometrika, 1, 211-218.
Gass, S.I., & Rapcsak, T. (2004). Singular value decomposition in AHP. European
Journal of Operational Research, 154, 573-584.
Geary, R.C. (1958). A note on the comparison of exchange rates and purchasing power
between countries. Journal of Royal Statistical Society, A 121, 97-99.
Khamis, S.H. (1972). A new system of index numbers for national and international
purposes. Journal of Royal Statistical Society, A 135, 96-121.
Kravis, I.B., Kenessey, Z., Heston, A.W., & Summers, R. (1975). A System of
International Comparisons of Gross Product and Purchasing Power. Baltimore, MD:
Johns Hopkins University Press.
Lipovetsky, S., & Tishler, A. (1994). Linear methods in multimode data analysis for
decision making. Computers and Operations Research, 21, 169-183.
Lipovetsky, S. (2007). Priority and choice probability estimation by ranking, rating, and
combined data, Journal of Statistical Theory and Practice, 1, 265-278.
Lipovetsky S. (2010). An interpretation of the AHP eigenvector solution for the lay
person. International Journal of the Analytic Hierarchy Process, 2, 158-162.
Lipovetsky S. (2011). An interpretation of the AHP global priority as the eigenvector
solution of an ANP supermatrix. International Journal of the Analytic Hierarchy
Process, 3, 70-78.
Rao, P., & Selvanathan, E.A. (1992). Computation of standard errors for Geary-Khamis
parities and international prices: a stochastic approach. Journal of Business & Economic
Statistics, 10, 109-115.
Saaty, T.L. (1994). Fundamentals of Decision Making and Priority Theory with the
Analytic Hierarchy Process. RWS Publications, Pittsburgh, PA.
ADDITIONAL BIBLIOGRAPHY
Lipovetsky S. and Conklin M. (2005). Singular value decomposition in additive,
multiplicative, and logistic forms. Pattern Recognition, 38, 1099-1110.
Lipovetsky, S. (2009). PCA and SVD with nonnegative loadings. Pattern Recognition,
42, 68-76.
Saaty, T.L. (1996). Decision Making with Dependence and Feedback: The Analytic
Network Process. RWS Publications, Pittsburgh, PA.
Saaty, T.L. (2008). The analytic hierarchy and analytic network measurement processes:
Applications to decisions under risk. European Journal of Pure and Applied
Mathematics, 1,122-196.
Saaty, T.L. (2009). Extending the measurement of tangibles to intangibles, International
Journal. of Information Technology & Decision Making, 8, 7-27.
Saaty, T.L. (2010). Principia Mathematica Decernendi: Mathematical Principles of
Decision Making: Generalization of the Analytic Network Process to Neural Firing and
Synthesis. RWS Publications, Pittsburgh, PA.
Saaty T.L., The Thinking Man’s New Millennium Joke Book, Part I, p.55.
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