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  • It is known that for basis linear fuzzy measures the Aumann and the Choquet integrals defined on a special class of fuzzy subsets of some Banach space commute. We characterize basis linear fuzzy measure by means of appropriate linear functionals, and consequently the relevant integral representation (by means of the Lebesgue integral) is introduced. As a corollary the well-known additivity of perimeters of convex subsets in the real plane is obtained.
  • It is known that for basis linear fuzzy measures the Aumann and the Choquet integrals defined on a special class of fuzzy subsets of some Banach space commute. We characterize basis linear fuzzy measure by means of appropriate linear functionals, and consequently the relevant integral representation (by means of the Lebesgue integral) is introduced. As a corollary the well-known additivity of perimeters of convex subsets in the real plane is obtained. (en)
  • Je známe, že pre bázové lineárne fuzzy miery komutujú Aumannov a Choquetov integrál, ktoré sú definované na špeciálnej triede fuzzy podmnožín nejakého Banachovho priestoru. V práci charakterizujeme bázové lineárne fuzzy miery pomocou vhodných lineárnych funkcionálov, a následne zavádzame príslušnú integrálnu reprezentáciu pomocou Lebesgueovho integrálu. Ako dôsledok dostávame známu aditivitu obvodov konvexnych podmnožín v reálnej rovine (cs)
Title
  • Linear non-additive set-functions
  • Linear non-additive set-functions (en)
  • Lineárne neaditívne množinové funkcie (cs)
skos:prefLabel
  • Linear non-additive set-functions
  • Linear non-additive set-functions (en)
  • Lineárne neaditívne množinové funkcie (cs)
skos:notation
  • RIV/67985556:_____/04:00106260!RIV/2005/GA0/A16005/N
http://linked.open.../vavai/riv/strany
  • 89;98
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA402/04/1026), Z(AV0Z1075907)
http://linked.open...iv/cisloPeriodika
  • 1
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  • 571584
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  • RIV/67985556:_____/04:00106260
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  • aumann integral;Choquet integral;fuzzy measure (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV
  • [2F475A329BC7]
http://linked.open...i/riv/nazevZdroje
  • International Journal of General Systems
http://linked.open...in/vavai/riv/obor
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http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 33
http://linked.open...iv/tvurceVysledku
  • Mesiar, Radko
  • Bouchon-Meunier, B.
  • Ralescu, D. A.
http://linked.open...n/vavai/riv/zamer
issn
  • 0308-1079
number of pages
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