The Weighted Least Square Method Applied to the Binary and Ternary AHP

  • Kazutomo Nishizawa
  • Iwaro Takahashi
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 4)


The weighted least square method is applied to the binary and ternary AHP (Analytic Hierarchy Process) based on the Bradley-Terry model. We transform this problem to have constant variance of errors (this is the basic property for the least square method to give the best estimators). The transformed problem has the form just to be solved by the geometric programming. Moreover the multi-stage Bradley-Terry model is proposed to meet the case where paired comparisons have various weights, which can also be solved by the geometric programming. Various examples solved by other methods are solved by our proposed method. The improved results are recognized.


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Copyright information

© Springer Berlin Heidelberg 2010

Authors and Affiliations

  • Kazutomo Nishizawa
    • 1
  • Iwaro Takahashi
    • 2
  1. 1.Nihon UniversityChibaJapan
  2. 2.University of Tsukuba, Tennodai, TsukubaIbarakiJapan

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