Pavluš, Miron; Tomeš, Rostislav; Malec, Lukáš Two proofs and one algorithm related to the analytic hierarchy process. (English) Zbl 1437.90089 J. Appl. Math. 2018, Article ID 5241537, 9 p. (2018). Summary: 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 \(\lambda_{\max}\) is equal to \(n\) for the eigenvector problem \(Aw = \lambda w\), where \(A\) is, so-called, the consistent matrix of pairwise comparisons of type \(n\times n(n\geq 2)\) 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. MSC: 90B50 Management decision making, including multiple objectives 91B06 Decision theory 15A18 Eigenvalues, singular values, and eigenvectors PDFBibTeX XMLCite \textit{M. Pavluš} et al., J. Appl. Math. 2018, Article ID 5241537, 9 p. (2018; Zbl 1437.90089) Full Text: DOI References: [1] Blachowski, J., Methodology for assessment of the accessibility of a brown coal deposit with Analytical Hierarchy Process and Weighted Linear Combination, Environmental Earth Sciences, 74, 5, 4119-4131 (2015) [2] Ossadnik, W.; Schinke, S.; Kaspar, R. H., Group Aggregation Techniques for Analytic Hierarchy Process and Analytic Network Process: A Comparative Analysis, Group Decision and Negotiation, 25, 2, 421-457 (2016) [3] Shih, C.-C.; Horng, R. S.; Lee, S.-K., Investigation of Lab Fire Prevention Management System of Combining Root Cause Analysis and Analytic Hierarchy Process with Event Tree Analysis, Mathematical Problems in Engineering, 2016 (2016) [4] Sivakumar, R.; Kannan, D.; Murugesan, P., Green vendor evaluation and selection using AHP and Taguchi loss functions in production outsourcing in mining industry, Resources Policy, 46, 64-75 (2015) [5] Kokangül, A.; Polat, U.; Dağsuyu, C., A new approximation for risk assessment using the AHP and Fine Kinney methodologies, Safety Science, 91, 24-32 (2017) [6] Peregrin, S.; Jablonsky, J., Analytic hierarchy process as a tool for group evaluation of healthcare equipment, International Journal of Business and Systems Research, 10, 2-4, 124-141 (2016) [7] Saaty, T. L., Mathematical Principles of Decision Making (Principia Mathematica Decernendi) (2010), Pittsburg, Calif, USA: RWS Publications, Pittsburg, Calif, USA [8] Saaty, T. L., The Analytic Hierarchy Process (1980), New York, NY, USA: McGraw-Hill, New York, NY, USA · Zbl 0587.90002 [9] Hobson, A. J., Just the MATHs (2002), Coventry, UK: Mathcentre, Coventry, UK [10] Vein, R.; Dale, P., Determinants and Their Application in Mathematical Physics (1999), New York, NY, USA: Springer, New York, NY, USA · Zbl 0913.15005 [11] Seman, J.; Litavcová, E.; Pavluš, M., Mathematics for Managers (2012), Prešov, Slovakia: Bookman, Prešov, Slovakia [12] Saaty, T. L., Decision-making with the AHP: why is the principal eigenvector necessary, European Journal of Operational Research, 145, 1, 85-91 (2003) · Zbl 1012.90015 [13] Xu, Y.; Wang, H., Eigenvector method, consistency test and inconsistency repairing for an incomplete fuzzy preference relation, Applied Mathematical Modelling, 37, 7, 5171-5183 (2013) · Zbl 1427.91106 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.