Fundamentals of the analytic network process — Dependence and feedback in decision-making with a single network

Abstract

The Analytic Network Process (ANP) is a multicriteria theory of measurement used to derive relative priority scales of absolute numbers from individual judgments (or from actual measurements normalized to a relative form) that also belong to a fundamental scale of absolute numbers. These judgments represent the relative influence, of one of two elements over the other in a pairwise comparison process on a third element in the system, with respect to an underlying control criterion. Through its supermatrix, whose entries are themselves matrices of column priorities, the ANP synthesizes the outcome of dependence and feedback within and between clusters of elements. The Analytic Hierarchy Process (AHP) with its independence assumptions on upper levels from lower levels and the independence of the elements in a level is a special case of the ANP. The ANP is an essential tool for articulating our understanding of a decision problem. One had to overcome the limitation of linear hierarchic structures and their mathematical consequences. This part on the ANP summarizes and illustrates the basic concepts of the ANP and shows how informed intuitive judgments can lead to real life answers that are matched by actual measurements in the real world (for example, relative dollar values) as illustrated in market share examples that rely on judgments and not on numerical data.

Keywords

Analytic Network Process (ANP) / decisions with feedback / interdependence / market share / paired-comparisons / supermatrix / limit priorities

References

[1] Blair A.R., Nachtmann R., Whitaker R., Saaty T.L.. Forecasting the resurgence of the US economy in 2001: An expert judgment approach. Socio-Economic Planning Sciences, 2002, 36(2): 77-91.

[2] Horn R.A., Johnson C.R.. Matrix Analysis, 1985, New York: Cambridge University Press

[3] Saaty, T.L., “Presidential elections, the superconducting supercollider, and organ transplant decisions”, pp345 in Multiple Criteria Decision Making, edited by A. Goicoechea, L. Duckstein, and S. Zionts, Springer-Verlag, 1992.

[4] Saaty T.L., Turner D.S.. Prediction of the 1996 super bowl. Proceedings of the Fourth International Symposium on the Analytic Hierarchy Process, 1996, Burnaby, B.C., Canada: Simon Fraser University

[5] Saaty T.L., Vargas L. G.. Models, Methods, Concepts and Applications of the Analytic Hierarchy Process, 2000, Boston: Kluwer Academic Publishers

[6] Saaty T.L.. Decision making — the Analytic Hierarchy and Network Processes (AHP/ANP). Journal of Systems Science and Systems Engineering, 2004, 13(1): 1-35.

[7] Saaty T.L.. The Analytic Network Process: Decision Making with Dependence and Feedback, 1996, 4922 Ellsworth Ave., Pittsburgh, PA 15213: RWS Publications

[8] SuperDecisions Software: www.superdecisions.com A program that is free to download and use for several months. For more information contact Creative Decisions Foundation, or email [e-mail].