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%3AN0000006" target="_blank" >RIV/26441021:_____/18:N0000006 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/26441021:_____/18:N0000030

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, 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, health-care, 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 n × n type with the solution w that represents the probability components of disjoint events. Moreover, we suggest an algorithm for the determination of the solution w of the eigenvalue problem Aw = nw as well as the corresponding flowchart. The algorithm for arbitrary consistent matrices A, n × n, (n ≥ 2) can be easily 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, 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, health-care, 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 n × n type with the solution w that represents the probability components of disjoint events. Moreover, we suggest an algorithm for the determination of the solution w of the eigenvalue problem Aw = nw as well as the corresponding flowchart. The algorithm for arbitrary consistent matrices A, n × n, (n ≥ 2) can be easily programmed and used.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

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OECD FORD obor

10100 - Mathematics

Projekt

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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

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Svazek periodika

—

Číslo periodika v rámci svazku

2018

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

9

Strana od-do

Nestrankovano

Kód UT WoS článku

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EID výsledku v databázi Scopus

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