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Proposal of Super Pairwise Comparison Matrix

  • Takao Ohya
  • Eizo Kinoshita
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 10)

Abstract

This paper proposes a Super Pairwise Comparison Matrix (SPCM) to express all pairwise comparisons in the evaluation process of the dominant analytic hierarchy process (AHP) or the multiple dominant AHP (MDAHP) as a single pairwise comparison matrix. In addition, this paper shows, by means of a numerical counterexample, that an evaluation value resulting from the application of the Harker method to a SPCM does not necessarily coincide with that of the evaluation value resulting from the application of the dominant AHP(DAHP) to the evaluation value obtained from each pairwise comparison matrix by using the eigenvalue method.

Keywords

pairwise comparison matrix dominant AHP logarithmic least square method Harker’s method 

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References

  1. 1.
    Saaty, T.L.: The Analytic Hierarchy Process. McGraw-Hill, New York (1980)zbMATHGoogle Scholar
  2. 2.
    Kinoshita, E., Nakanishi, M.: Proposal of new AHP model in light of do-minative re-lationship among alternatives. Journal of the Operations Research Society of Japan 42, 180–198 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Kinoshita, E., Sekitani, K., Shi, J.: Mathematical Properties of Dominant AHP and Concurrent Convergence Method. Journal of the Operations Research Society of Japan 45, 198–213 (2002)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Harker, P.T.: Incomplete pairwise comparisons in the Analytic Hierarchy Process. Mathematical Modeling 9, 837–848 (1987)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Takao Ohya
    • 1
  • Eizo Kinoshita
    • 2
  1. 1.School of Science and EngineeringKokushikan UniversityTokyoJapan
  2. 2.Faculty of Urban ScienceMeijo UniversityGifuJapan

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