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Published Dec 31, 2010
Stan Lipovetsky

Abstract

An AHP priority vector represents the importance, preference, or likelihood of its elements with respect to a certain property or criterion and here we examine how that priority vector can be derived through an iterative process applied to the pairwise comparison matrix. Further, we show that the vector obtained in this way satisfies the definition for an eigenvector of the original judgment matrix. Practical managers using AHP in decision making would most likely be better able to appreciate this approach than they would a process phrased in the language of linear algebra. The overall priority vector for the alternatives in a hierarchy and, further, in a network, can be obtained in the same way by applying the iterative process to the supermatrix of the ANP. This claim is examined in depth in a forthcoming paper that will appear in this journal.


http://dx.doi.org/10.13033/ijahp.v2i2.42

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Keywords

AHP priority vectors, AHP pairwise comparison eigenvector, AHP supermatrix eigenvector

References
Golden, B.L., Wasil, E.A., & Harker, P.T. (eds.), (1989). The Analytic Hierarchy
Process: Applications and Studies. Berlin-Heidelberg: Springer.
Lipovetsky, S. (1996). The synthetic hierarchy method: an optimizing approach to a
obtaining priorities in the AHP. European Journal of Operational Research, 93, 550-564.
Lipovetsky, S., & Tishler, A. (1999). Interval estimation of priorities in the AHP.
European Journal of Operational Research, 114, 153-164.
Lipovetsky, S., & Conklin, M. (2002). Robust estimation of priorities in the AHP.
European Journal of Operational Research, 137, 110-122.
Lipovetsky, S. (2005). Analytic hierarchy processing in Chapman-Kolmogorov
equations. International J. of Operations and Quantitative Management, 11, 219-228.
Lipovetsky, S. (2008). Comparison among different patterns of priority vectors
estimation methods. International J. of Mathematical Education in Science and
Technology, 39, 301-311.
Lipovetsky, S. (2009a). Global priority estimation in multiperson decision making.
Journal of Optimization Theory and Applications, 140, 77-91.
Lipovetsky, S. (2009b). Optimal hierarchy structures for multi-attribute-criteria decisions.
Journal of Systems Science and Complexity, 22, 228-242.
Saaty, T.L. (1977). A scaling method for priorities in hierarchical structures.
Mathematical Psychology, 15, 234-281.
Saaty, T.L. (1980). The Analytic Hierarchy Process. New York: McGraw-Hill.
Saaty, T.L. (1994). Fundamentals of Decision Making and Priority Theory with the
Analytic Hierarchy Process. Pittsburgh, PA: RWS Publications.
Saaty, T.L. (1996). Decision Making with Dependence and Feedback: The Analytic
Network Process. Pittsburgh, PA: RWS Publications.
Saaty, T.L. (2000). Decision Making for Leaders. Pittsburgh, PA: RWS Publications.
Saaty, T.L. (2010). Principia Mathematica Decernendi: Mathematical Principles of
Decision Making: Generalization of the Analytic Network Process to Neural Firing and
Synthesis. Pittsburgh, PA: RWS Publications.
Saaty, T.L., & Kearns, K.P. (1985). Analytical Planning. New York: Pergamon Press.
Saaty, T.L., & Vargas, L.G. (1994). Decision Making in Economic, Political, Social and
Technological Environment with the Analytic Hierarchy Process. Pittsburgh, PA: RWS
Publications.
The Wisdom of the Fathers, and its classical commentaries (1960). Translated by Y.
Goldin, New York: The Heritage Press.
Wasil, E.A., & Golden, B.L. (2003). Celebrating 25 years of AHP-based decision
making. Computers and Operations Research, 30, 1419-1420.
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