Preference matrices in tropical algebra

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18450%2F13%3A50001779" target="_blank" >RIV/62690094:18450/13:50001779 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Preference matrices in tropical algebra

Popis výsledku v původním jazyce

Relative importance of alternatives in AHP multi-criteria decision problem is standardly computed from the (possibly incosistent) preference matrix as the eigenvector of the preference matrix by methods of linear algebra. Alternative use of non-standardmethods in other algebras, such as tropical or fuzzy algebra is considered in this paper. The preference matrix is investigated by the methods used in max-prod algebra. Given preference matrix is processed by max-prod operations, until a steady state isreached. The eigenvector of the matrix then describes the steady state preferences and respects all preference relations contained in the original matrix. Efficient algorithms for computing eigenvectors in the tropical algebra are described. The method is illustrated by numerical examples and compared with the linear algebra approach. The consistent and inconsistent cases are considered.

Název v anglickém jazyce

Preference matrices in tropical algebra

Popis výsledku anglicky

Relative importance of alternatives in AHP multi-criteria decision problem is standardly computed from the (possibly incosistent) preference matrix as the eigenvector of the preference matrix by methods of linear algebra. Alternative use of non-standardmethods in other algebras, such as tropical or fuzzy algebra is considered in this paper. The preference matrix is investigated by the methods used in max-prod algebra. Given preference matrix is processed by max-prod operations, until a steady state isreached. The eigenvector of the matrix then describes the steady state preferences and respects all preference relations contained in the original matrix. Efficient algorithms for computing eigenvectors in the tropical algebra are described. The method is illustrated by numerical examples and compared with the linear algebra approach. The consistent and inconsistent cases are considered.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BB - Aplikovaná statistika, operační výzkum

OECD FORD obor

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Projekt

<a href="/cs/project/GA402%2F09%2F0405" target="_blank" >GA402/09/0405: Rozvoj nestandardních optimalizačních metod a jejich aplikace v ekonomii a managementu</a><br>

Návaznosti

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název periodika

International symposium on the analytic hierarchy process

ISSN

1556-830X

e-ISSN

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Svazek periodika

neuveden

Číslo periodika v rámci svazku

červenec

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

7

Strana od-do

1-7

Kód UT WoS článku

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EID výsledku v databázi Scopus

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