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2018 Two Proofs and One Algorithm Related to the Analytic Hierarchy Process
Miron Pavluš, Rostislav Tomeš, Lukáš Malec
J. Appl. Math. 2018: 1-9 (2018). DOI: 10.1155/2018/5241537


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 λ m a x is equal to n for the eigenvector problem A w = λ w , 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 A w = n w as well as the corresponding flowchart. The algorithm for arbitrary consistent matrix A can be simply programmed and used.


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Miron Pavluš. Rostislav Tomeš. Lukáš Malec. "Two Proofs and One Algorithm Related to the Analytic Hierarchy Process." J. Appl. Math. 2018 1 - 9, 2018.


Received: 30 April 2018; Revised: 1 August 2018; Accepted: 23 August 2018; Published: 2018
First available in Project Euclid: 10 January 2019

zbMATH: 07051365
MathSciNet: MR3892180
Digital Object Identifier: 10.1155/2018/5241537

Rights: Copyright © 2018 Hindawi


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