Published Dec 26, 2017
Min-Suk Yoon


In order to honor Thomas Saaty, the developer of Analytic Hierarchy Process (AHP)/ Analytic Network Process (ANP), and focus on the paper he wrote just before he died, this essay mentions the rank order problem due to the addition/deletion of irrelevant alternatives over which there were controversies in the AHP. Saaty ended the controversies with the explanation that both rank preservation and rank reversal are possible depending on the decision making circumstance. In this paper, we will summarize the three properties that fundamentally act on how to prioritize and aggregate the subjective judgments of human beings in ranking alternatives: comparisons, judgmental dependency and rank order. This essay also mentions the rank order in relation to the cases of addition/deletion of irrelevant criteria from previous studies. This essay closes by expressing gratitude to Thomas Saaty for his work.


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decision making, rank preservation, rank reversal, subjective judgment, comparisons

Millet, I. & Saaty, T.L. (2000). On the relativity of relative measures—accommodating both rank preservation and rank reversals in the AHP. European Journal of Operational Research, 121, 205-212. Doi:

Saaty T. L. (2015). Rank preservation and reversal in decision making. Journal of Advances in Management Sciences & Information Systems, 1, 34-37.
Saaty T. L., Vargas, L.G. & Whitaker, R. (2009). Addressing with brevity criticisms of the Analytic Hierarchy Process, International Journal of the Analytic Hierarchy Process, 1(2), 121-134. Doi:
Yoon, M.S. & Kinoshita, E. (2009). Classification of the Analytic Hierarchy Process approaches by application circumstances, International Journal of Management Science, 16(1), 17-47.