Preference matrices in tropical algebra
The result's identifiers
Result code in 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>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Preference matrices in tropical algebra
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BB - Applied statistics, operational research
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA402%2F09%2F0405" target="_blank" >GA402/09/0405: Development of Non-standard Optimization Methods and their Applications in Economy and Management</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International symposium on the analytic hierarchy process
ISSN
1556-830X
e-ISSN
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Volume of the periodical
neuveden
Issue of the periodical within the volume
červenec
Country of publishing house
US - UNITED STATES
Number of pages
7
Pages from-to
1-7
UT code for WoS article
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EID of the result in the Scopus database
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