title: Methods of tropical optimization in multicriteria problems of raiting alternatives from pairwise comparisons
metadata.name: dc.contributor.author
metadata.value: Krivulin, Nikolai K.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Ageev, Vladimir A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-03-05T12:00:09Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-03-05T12:00:09Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Krivulin N. K., Ageev V. A. Methods of tropical optimization in multicriteria problems of raiting alternatives from pairwise comparisons. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2019, vol. 15, iss. 4, pp. 472–488.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2019.405
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17158
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The paper deals with the application of methods and results of tropical mathematics, which
  focuses on the theory and applications of algebraic systems with idempotent operations, to
  the development of a multicriteria decision-making procedure. A problem is considered to
  evaluate ratings of alternatives from pairwise comparisons of the alternatives under several
  criteria, and from pairwise comparisons of the criteria. To solve the problem, a decisionmaking
  procedure is proposed based on the Chebyshev approximation, in logarithmic scale,
  of pairwise comparison matrices by reciprocally symmetrical matrices of unit rank (consistent
  matrices), which determine the elements in the vectors of weights of criteria and ratings of
  alternatives. First, the approximation problem for the matrix of pairwise comparison of
  criteria is solved to find the weights of criteria. Then, the weighted pairwise comparison matrices of alternatives are approximated by a common consistent matrix, which gives
  the required vector of ratings of alternatives. If the result is not unique (up to a positive
  factor), an additional problem of analyzing the solutions is solved to find vectors that can
  be considered, in a sense, as the worst and best solutions. In the framework of the proposed
  procedure, the problems of approximation and analysis of solutions are formulated as tropical
  optimization problems, which have direct analytical solutions in a compact vector form. An
  example of the application of the procedure to solve the known problem by T. Saaty on
  selecting a school is given.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work was supported by the Russian Foundation for Basic Reaserch (grant N18-010-00723).
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 15; Issue 4
metadata.lang: -
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: matrix approximation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: log-Chebyshev metric
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: multicretiria decision making problem
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Methods of tropical optimization in multicriteria problems of raiting alternatives from pairwise comparisons
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 472-488.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17158/1/472-488.pdf
resources.format: Adobe PDF
resources.size: 337,63 kB