Normalization Method Based on Dummy Alternative with Perfect Evaluation Score in AHP and ANP

  • Kazutomo Nishizawa
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 15)


In this paper an appropriate normalization method for alternatives in the Analytic Hierarchy Process (AHP) and the Analytic Network Process (ANP) is proposed. In the traditional AHP, in general, we calculate the principal eigenvalue and the corresponding eigenvector from a pairwise comparison matrix. By normalizing the sum of eigenvector to 1, we obtain the weights of alternatives. However, this normalization method is considered as one of the causes of some problems, for example rank reversal etc.. Therefore, at first in this paper, the verification example for verify the normalization methods is shown and also the correct value of this example is shown. Using this example, at secondly, some normalization problems are pointed out. Based on the incorrect results, at thirdly, an appropriate normalization method based on artificially added dummy alternative with the perfect evaluation score is proposed. Applying proposed method to the verification example for the AHP and the two-cluster ANP, the accurate result is obtained. Finally, proposed normalization method is concluded by considering the result from the verification example.


Analytic Hierarchy Process Normalization Method Comparison Matrix Analytic Network Process Incorrect Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Nihon UniversityNarashinoJapan

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