Two proofs and one algorithm related to the analytic hierarchy process

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F26441021%3A_____%2F18%3AN0000030" target="_blank" >RIV/26441021:_____/18:N0000030 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/26441021:_____/18:N0000006

Výsledek na webu

<a href="https://www.hindawi.com/journals/jam/2018/5241537/" target="_blank" >https://www.hindawi.com/journals/jam/2018/5241537/</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1155/2018/5241537" target="_blank" >10.1155/2018/5241537</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Two proofs and one algorithm related to the analytic hierarchy process

Popis výsledku v původním jazyce

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 max is equal to n for the eigenvector problem Aw=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 Aw=nw as well as the corresponding flowchart. The algorithm for arbitrary consistent matrix A can be simply programmed and used.

Název v anglickém jazyce

Two proofs and one algorithm related to the analytic hierarchy process

Popis výsledku anglicky

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 max is equal to n for the eigenvector problem Aw=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 Aw=nw as well as the corresponding flowchart. The algorithm for arbitrary consistent matrix A can be simply programmed and used.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

—

Návaznosti

N - Vyzkumna aktivita podporovana z neverejnych zdroju

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Applied Mathematics

ISSN

1110-757X

e-ISSN

1687-0042

Svazek periodika

2018

Číslo periodika v rámci svazku

2018

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

9

Strana od-do

—

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85058941389