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Analytic Hierarchy Process

  1. Thomas L. Saaty

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a4a002

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Saaty, T. L. 2005. Analytic Hierarchy Process. Encyclopedia of Biostatistics. 1.

Author Information

  1. University of Pittsburgh, Pittsburgh, PA, USA

Publication History

  1. Published Online: 15 JUL 2005


The Analytic Hierarchy Process (AHP) is a theory of relative measurement of intangible criteria. With this approach to relative measurement, a scale of priorities is derived from pairwise comparison measurements only after the elements to be measured are known. The ability to do pairwise comparisons is our biological heritage and we need it to cope with a world where everything is relative and constantly changing and thus, there are no fixed standards to measure things on. In traditional measurement, one has a scale that one applies to measure any element that comes along that has the property the scale is for, and the elements are measured one by one, not by comparing them with each other. In the AHP, paired comparisons are made with judgments using numerical values taken from the AHP absolute fundamental scale of 1 to 9. A scale of relative values is derived from all these paired comparisons and it also belongs to an absolute scale that is invariant under the identity transformation like the system of real numbers. The AHP is useful for making multicriteria decisions involving benefits, opportunities, costs, and risks. The ideas are developed in stages and illustrated with examples of real-life decisions. The subject is transparent and easy to understand why it is done the way it is along the lines discussed here. The AHP has a generalization to dependence and feedback; the Analytic Network Process (ANP) is not discussed here.


  • analytic hierarchy process;
  • decision making;
  • prioritization;
  • benefits;
  • costs;
  • complexity