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Two Proofs and One Algorithm Related to the Analytic Hierarchy Process

Author

Listed:
  • Miron Pavluš
  • Rostislav Tomeš
  • Lukáš Malec

Abstract

36 years ago, Thomas Saaty introduced a new mathematical methodology, called Analytic Hierarchy Process (AHP), regarding the decision‐making processes. The methodology was widely applied by Saaty and by other authors in the different human activity areas, like planning, business, education, healthcare, etc. but, in general, in the area of management. In this paper, we provide two new proofs for well‐known statement that the maximal eigenvalue λmax is equal to n for the eigenvector problem Aw = λw, where A is, so‐called, the consistent matrix of pairwise comparisons of type n × n (n≥ 2) with the solution vector w that represents the probability components of disjoint events. Moreover, we suggest an algorithm for the determination of the eigenvalue problem solution Aw = nw as well as the corresponding flowchart. The algorithm for arbitrary consistent matrix A can be simply programmed and used.

Suggested Citation

  • Miron Pavluš & Rostislav Tomeš & Lukáš Malec, 2018. "Two Proofs and One Algorithm Related to the Analytic Hierarchy Process," Journal of Applied Mathematics, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnljam:v:2018:y:2018:i:1:n:5241537
    DOI: 10.1155/2018/5241537
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    References listed on IDEAS

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    1. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
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    4. Cheng-Chan Shih & Richard S. Horng & Shin-Ku Lee, 2016. "Investigation of Lab Fire Prevention Management System of Combining Root Cause Analysis and Analytic Hierarchy Process with Event Tree Analysis," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-12, June.
    5. Sivakumar, R. & Kannan, Devika & Murugesan, P., 2015. "Green vendor evaluation and selection using AHP and Taguchi loss functions in production outsourcing in mining industry," Resources Policy, Elsevier, vol. 46(P1), pages 64-75.
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