title: Application of methods of tropical optimization for evaluating alternatives based on pairwise comparisons
metadata.name: dc.contributor.author
metadata.value: Krivulin, Nikolai Kimovich
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Ageev, Vladimir Anatolyevich
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Gladkikh, Igor Valentiniovich
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-05-18T12:18:15Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-05-18T12:18:15Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Krivulin N. K., Ageev V. A., Gladkikh I. V. Application of methods of tropical optimization for evaluating alternatives based on pairwise comparisons. Vestnik of Saint Petersburg University. Applied mathematics. Computer science. Control processes, 2017, volume 13, issue 1, pp. 27– 41.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu10.2017.103
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/6350
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Solution to the problem of evaluating alternatives based on pairwise comparisons is considered,
  using methods of tropical optimization. The problem of deriving the vector of scores for
  alternatives reduces to the approximation of pairwise comparison matrices by consistent
  matrices in the sense of the log-Chebyshev metric. Then the approximation problem is
  formulated and solved in terms of tropical mathematics. The results obtained are represented
  in compact vector form, ready for further analysis and practical computations. In the case when
  the solution is non-unique (up to a positive factor), it is suggested that the set of solutions be
  characterized via two solutions that are, in some sense, the best and worst solutions. As the best solution, the vector is taken which best differentiates between the alternatives with the highest
  and lowest scores, and as the worst, the vector which worth differentiates these alternatives. It is
  shown that these vectors can be obtained using methods of tropical optimization. To illustrate
  the results obtained, solution examples for problems of evaluating the scores of alternatives are
  given. Refs 23.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке Российского гуманитарного научного фонда
  (проект № 16-02-00059).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 13; Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: tropical mathematics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: idempotent semifield
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: tropical optimization
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: pairwise comparison matrix
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: consistent matrix
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: log-Chebyshev metric
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: matrix approximation
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Application of methods of tropical optimization for evaluating alternatives based on pairwise comparisons
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 03-Krivulin.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/6350/1/03-Krivulin.pdf
resources.format: Adobe PDF
resources.size: 272,81 kB