title: Algebra of fuzzy numbers with unimodal membership function
metadata.name: dc.contributor.author
metadata.value: Germashev, Ilya V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Derbisher, Evgeniya V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Derbisher, Vyacheslav E.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Kartashova, Anna V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Titov, Alexander V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-12-27T12:21:44Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-12-27T12:21:44Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Germashev I.V., Derbisher E.V., Derbisher V.E., Kartashova A.V., Titov A.V. Algebra of fuzzy numbers with unimodal membership function. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 4, pp. 590–601. https://doi.org/10.21638/spbu01.2022.402 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.402
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/38714
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Fuzzy numbers with a unimodal membership function are presented, which have found
  application in the fuzzy analysis of such subject fields as ecology, chemical technology. In
  this article, a set of fuzzy numbers with an unimodal membership function of a special type
  is considered. Two binary operations (addition and multiplication) are given over this set,
  formulas for calculation are obtained and some properties of this algebra are investigated.
  It is proved that addition and multiplication are commutative and associative. Moreover,
  multiplication is distributive over addition. It is shown that there are no neutral and inverse
  elements over both operations. Note that if we add neutral elements under addition and
  multiplication to the given algebra, we will obtain a commutative semiring. The conditions
  under which quasineutral or quasiinverse elements exist are also given.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work is supported by state task of the Ministry of Science and Higher Education of Russia
  (project no. 0633-2020-0003).
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. Mathematics. Mechanics. Astronomy;Volume 9 (67); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: algebra
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: fuzzy numbers
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: arithmetic operations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: associativity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: distributivity
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Algebra of fuzzy numbers with unimodal membership function
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 590-601.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/38714/1/590-601.pdf
resources.format: Adobe PDF
resources.size: 295,2 kB