Advertisement

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)

Abstract

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.

Keywords

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Belton, V., Gear, T.: On a Short-comming of Saaty’s method of Analytic Hierarchies. Omega 11, 228–230 (1983)CrossRefGoogle Scholar
  2. 2.
    Belton, V., Gear, T.: The legitimacy of rank reversal – A comment. Omega 13, 143–145 (1985)CrossRefGoogle Scholar
  3. 3.
    Kinoshita, E., Nakanishi, M.: Proposal of new AHP model in light of dominant relationship among alternatives. Journal of the Operations Research Society of Japan 42, 180–197 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Kinoshita, E., Sugiura, S.: A comparison study of dominant AHP and similar dominant models. Journal of Research Institute of Meijo University 7, 115–116 (2008)Google Scholar
  5. 5.
    Nishizawa, K.: Simple AHP based on three-level evaluation and two-cluster ANP for the decision makers. Journal of Japanese Symposium on The Analytic Hierarchy Process 1, 97–104 (2007) (in Japanese)Google Scholar
  6. 6.
    Nishizawa, K.: Two-cluster ANP which consists of the evaluation sub-matrix of the alternatives and its transposed matrix instead of pair-wise comparisons among the criteria. Journal of Japanese Symposium on The Analytic Hierarchy Process 2, 59–67 (2010)Google Scholar
  7. 7.
    Saaty, T.L.: The Analytic Hierarchy Process. McGraw-Hill, New York (1980)zbMATHGoogle Scholar
  8. 8.
    Saaty, T.L.: The Analytic Network Process. RWS Publications, Pittsburgh (1996)Google Scholar
  9. 9.
    Schoner, B., Wedley, W.C.: Ambiguous criteria weights in AHP: Consequences and solutions. Decision Sciences 20, 462–475 (1989)CrossRefGoogle Scholar
  10. 10.
    Schoner, B., Wedley, W.C., Choo, E.U.: A unified approach to AHP with linking pins. European Journal of Operational Research 13, 384–392 (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Nihon UniversityNarashinoJapan

Personalised recommendations