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Two Proofs and One Algorithm Related to the Analytic Hierarchy Process
Joint Authors
Pavluš, Miron
Tomeš, Rostislav
Malec, Lukáš
Source
Journal of Applied Mathematics
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-12-02
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Pavluš, Miron& Tomeš, Rostislav& Malec, Lukáš. 2018. Two Proofs and One Algorithm Related to the Analytic Hierarchy Process. Journal of Applied Mathematics،Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1176026
Modern Language Association (MLA)
Pavluš, Miron…[et al.]. Two Proofs and One Algorithm Related to the Analytic Hierarchy Process. Journal of Applied Mathematics No. 2018 (2018), pp.1-9.
https://search.emarefa.net/detail/BIM-1176026
American Medical Association (AMA)
Pavluš, Miron& Tomeš, Rostislav& Malec, Lukáš. Two Proofs and One Algorithm Related to the Analytic Hierarchy Process. Journal of Applied Mathematics. 2018. Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1176026
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1176026