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| Description
| - In AHP approach to multi-criteria decision problem, the relative importance of alternatives is computed from preference matrices, which come from experience and can possibly be inconsistent. Standardly, the prefference vector is computed as the eigenvector of the preference matrix by methods of linear algebra. Alternative use of non-standard methods in tropical algebra is considered in this paper. Two most frequently used tropical algebras are the max-plus and the max-prod algebra. The preference matrix will be processed by the methods used in max-prod algebra. By max-prod algebra we understand a linear structure on a linearly ordered set R of real numbers together with the binary operations \oplus= maximum and \otimes = product, similarly as the ordinary addition and multiplication operations are used in the classical linear algebra. The operations \oplus and \otimes are extended to matrices and vectors in a natural way. We should remark that the max-prod algebra is isomorphic to max-plus algebra, with the operations maximum and addition. The eigenvalue of a given max-plus or max-prod matrix and the eigenvectors can be eciently described by considering cycles in speci cally evaluated directed graphs. Given preference matrix will be transformed by the tropical operations, until a steady state is reached. The eigenvector of the matrix then describes the steady state references and respects all preference relations contained in the original matrix. Efficient algorithmsfor 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.
- In AHP approach to multi-criteria decision problem, the relative importance of alternatives is computed from preference matrices, which come from experience and can possibly be inconsistent. Standardly, the prefference vector is computed as the eigenvector of the preference matrix by methods of linear algebra. Alternative use of non-standard methods in tropical algebra is considered in this paper. Two most frequently used tropical algebras are the max-plus and the max-prod algebra. The preference matrix will be processed by the methods used in max-prod algebra. By max-prod algebra we understand a linear structure on a linearly ordered set R of real numbers together with the binary operations \oplus= maximum and \otimes = product, similarly as the ordinary addition and multiplication operations are used in the classical linear algebra. The operations \oplus and \otimes are extended to matrices and vectors in a natural way. We should remark that the max-prod algebra is isomorphic to max-plus algebra, with the operations maximum and addition. The eigenvalue of a given max-plus or max-prod matrix and the eigenvectors can be eciently described by considering cycles in speci cally evaluated directed graphs. Given preference matrix will be transformed by the tropical operations, until a steady state is reached. The eigenvector of the matrix then describes the steady state references and respects all preference relations contained in the original matrix. Efficient algorithmsfor 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. (en)
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| Title
| - Decision making in max-prod algebra
- Decision making in max-prod algebra (en)
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| skos:prefLabel
| - Decision making in max-prod algebra
- Decision making in max-prod algebra (en)
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| skos:notation
| - RIV/62690094:18450/13:50001777!RIV14-GA0-18450___
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| http://linked.open...avai/predkladatel
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
| - I, P(EE2.3.20.0001), P(GA402/09/0405), S
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
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| http://linked.open...ai/riv/idVysledku
| - RIV/62690094:18450/13:50001777
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| http://linked.open...riv/jazykVysledku
| |
| http://linked.open.../riv/klicovaSlova
| - algorithm; eigenproblem; multi-criteria decision making; max-prod algebra (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...v/mistoKonaniAkce
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| http://linked.open...i/riv/mistoVydani
| |
| http://linked.open...i/riv/nazevZdroje
| - Czech-Japan seminar on data analysis and decision making under uncertainty : proceedings
|
| http://linked.open...in/vavai/riv/obor
| |
| http://linked.open...ichTvurcuVysledku
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| http://linked.open...cetTvurcuVysledku
| |
| http://linked.open...vavai/riv/projekt
| |
| http://linked.open...UplatneniVysledku
| |
| http://linked.open...iv/tvurceVysledku
| - Gavalec, Martin
- Tomášková, Hana
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| http://linked.open...vavai/riv/typAkce
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| http://linked.open.../riv/zahajeniAkce
| |
| number of pages
| |
| http://purl.org/ne...btex#hasPublisher
| - Vysoká škola ekonomická. Fakulta managementu
|
| https://schema.org/isbn
| |
| http://localhost/t...ganizacniJednotka
| |
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