TY - JOUR
A2 - Hong, Wei-Chiang
AU - Pavluš, Miron
AU - Tomeš, Rostislav
AU - Malec, Lukáš
PY - 2018
DA - 2018/12/02
TI - Two Proofs and One Algorithm Related to the Analytic Hierarchy Process
SP - 5241537
VL - 2018
AB - 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.
SN - 1110-757X
UR - https://doi.org/10.1155/2018/5241537
DO - 10.1155/2018/5241537
JF - Journal of Applied Mathematics
PB - Hindawi
KW -
ER -