Abstract
In this paper we give a skeletal outline of the foundations of the Analytic Hierarchy Process and some of its highlights. We also show that the principal eigenvector solution is essential for deriving the scale of priorities from the fundamental scale of judgments given in the matrix.
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13 February 2021
A Correction to this paper has been published: https://doi.org/10.1007/s41237-020-00125-5
References
Aczel, J. and Saaty, T.L. (1983). Procedures for synthesizing ratio judgements; Journal of Mathematical Psychology, 27, 93–102.
Expert Choice; Software package, Decision Support Software, McLean, VA.
Saaty, T.L. (1980). The Analytic Hierarchy Process; McGraw Hill Internationa], p. 287.
Saaty, T.L. (1984). Decision Making for Leaders; Wadsworth.
Saaty, T.L. (1986). Axiomatic foundation of the analytic hierarchy process; Management Science, 32, 841–855.
Saaty, T.L. Absolute and Relative Measurement with the AHP: the Most Livable Cities in the U.S., Socio-Economic.
Saaty, T.L. (1987). Rank Generation, Preservation and Reversal in the Analytic Hierarchy Process; Decision Sciences, July.
Saaty, T.L. (1987). Rank According to Perron; Mathematics Magazine, Oct.
Saaty, T.L. and Kearns, K.P. (1985). Analytical Planning; Pergamon Press, p. 208.
Saaty, T.L. and Vargas, L.G. (1981). The Logics of Priorities, Applications in Business, Energy, Health, Transportation; Kluwer-Nijhoff Publishing, p. 299.
Saaty, T.L. and Vargas, L.G. (1984). Inconsistency and rank preservation; Journal of Mathematical Psychology, 28, 205–214.
Saaty, T.L. and Vargas, L.G. (1987). Stimulus-response with reciprocal kernels: the rise and fall of sensation; Journal of Mathematical Psychology, March.
Vargas, L.G. (1982). Reciprocal matrices with random coefficients; Journal of Mathematical Modelling, 3, 69–81.
Xu, S. (1986). References on the Analytic Hierarchy Process; Institute of Systems Engineering, Tianjin University, June.
Zahedi, F. (1986). The Analytic hierarchy process — A survey of the method and its applications; Interfaces, 16(4).
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Saaty, T.L. Some Mathematical Concepts of the Analytic Hierarchy Process. Behaviormetrika 18, 1–9 (1991). https://doi.org/10.2333/bhmk.18.29_1
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DOI: https://doi.org/10.2333/bhmk.18.29_1