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Published Jun 14, 2011
Stan Lipovetsky

Abstract

Not only the local priority vectors but also the global synthesized priority vector for the alternatives can be obtained from the eigenproblem solution for the ANP supermatrix. This global priority vector retains the main property of any AHP vector – to present the mean dominance of each of the items over the others with respect to the goal of the hierarchy.


http://dx.doi.org/10.13033/ijahp.v3i1.90

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Keywords

AHP local and global vectors, ANP, eigenproblem of supermatrix

References
Lipovetsky, S. (1996). The synthetic hierarchy method: an optimizing approach to
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. (2010). An interpretation of the AHP eigenvector solution for the lay
person. IJAHP, 2/2, 159-162.
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. (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.
Appendix I. Additional bibliography
Bernasconi M., Choirat C. and Seri R. (2010). The analytic hierarchy process and the
theory of measurement. Management Science, 56, 699-711.
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. (2000). Decision Making for Leaders. Pittsburgh, PA: RWS Publications.
Saaty, T.L. (2008a). 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. (2008b). Relative measurement and its generalization in decision making –
why pairwise comparisons are central in mathematics for the measurement of intangible
factors:
The Analytic Hierarchy/Network Process, RACSAM Rev. R. Acad. Cien. Ser. A. Mat.,
102, 251–318.
Vaidya O.S. and Kumar S. (2006). Analytic hierarchy process: An overview of
applications. European Journal of Operational Research, 169, 1-29.
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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