Reply to "Remarks on the Analytic Hierarchy Process" by J. S. Dyer (original) (raw)
Journal of Applied Information Science, 2017
In this paper, we first reviews different measurement scales (Linear, Power, Geometric, Logarithmic, Root square, Inverse linear, and Balanced) adopted in Analytic Hierarchy Process (AHP). then, with reduction of different measurement scale ranges to: left position (i.e., for linear measurement scale: 1-3), middle position (4-6), right position (7-9), left & middle position (1-6), middle & right position (4-9), and perfect ranges (1-9), the effects of different measurement scale on priorities and discrimination level (to discriminate an important alternative from others) of alternatives are investigated. The findings of this paper reveal that first, in 39 possibilities out of 42 cases, the same ranking (A1>A2>A3) with different intensities were obtained, and in 3 possibilities rank reversal are happened. Next, the geometric measurement scale in all ranges and particularly in perfect range have the best performance in discriminating an important alternative than others. Moreover, only the left position and perfect ranges in the most of measurement scales have the best performance in discriminating an important alternative from others.
The Analytic Hierarchy Process and the Theory of Measurement
The analytic hierarchy process (AHP) is a decision-making procedure widely used in management for establishing priorities in multicriteria decision problems. Underlying the AHP is the theory of ratio-scale measures developed in psychophysics since the middle of the last century. It is, however, well known that classical ratio-scaling approaches have several problems. We reconsider the AHP in the light of the modern theory of measurement based on the so-called separable representations recently axiomatized in mathematical psychology. We provide various theoretical and empirical results on the extent to which the AHP can be considered a reliable decision-making procedure in terms of the modern theory of subjective measurement.