Published Dec 26, 2017
Birsen Karpak


This article discusses my reflections on Mathematical Principles of Decision Making by Thomas Saaty  (Saaty T. L., 2010). In this book, Saaty very clearly explains his Analytic Hierarchy Process (AHP) theory for measuring both tangible and intangible factors. Experts judgments are elicited about the dominance of a factor over another one via pairwise comparisons using an absolute scale and priorities of the factors are derived. The important concepts of the AHP such as compatibility index, validation, sensitivity analysis for testing the robustness of the priorities derived, and its generalization to structures with dependence and feedback, and the Analytic Network Process (ANP) are given. Extensions of the theory to complex decisions involving benefits, opportunities, costs and risks and applications to resource allocation and conflict resolution are included, as well as the generalization to continuous and time dependent judgments is also covered.



How to Cite

Karpak, B. (2017). REFLECTIONS: MATHEMATICAL PRINCIPLES OF DECISION MAKING. International Journal of the Analytic Hierarchy Process, 9(3).


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AHP, ANP, BOCR, dynamic priorities, continuous judgments, resource allocation, conflict resolution

Saaty, T. L. (2010). Mathematical principles of decisions making. Pittsburgh: RWS Publications.
Saaty, T. L., & Shih, H. S. (2009). Structures in decision making: On the subjective geometry of hierarchies and networks. European Journal of Operations Research, 199(3), 867-872. Doi:

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