A universal integral

Erich Peter Klement, Radko Mesiar, E. Pap

Research output: Chapter in Book/Report/Conference proceedingConference contribution

14 Citations (Scopus)

Abstract

Based on a minimal set of axioms we introduce a general integral which can be defined on arbitrary measurable spaces. It acts on measures which are only (finite) monotone set functions and on measurable functions whose range is contained in the unit interval. We introduce the notion of integral equivalence of pairs of measures and functions which leads us to a special important general integrals called universal integral. Several special types of such functionals, including extremal ones, are characterized.

Original languageEnglish
Title of host publicationNew Dimensions in Fuzzy Logic and Related Technologies - Proceedings of the 5th EUSFLAT 2005 Conference
Pages253-256
Number of pages4
Volume1
Publication statusPublished - 2007
Event5th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2007 - Ostrava, Czech Republic
Duration: Sep 11 2007Sep 14 2007

Other

Other5th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2007
CountryCzech Republic
CityOstrava
Period9/11/079/14/07

Keywords

  • Choquet integral
  • General integral
  • Integral equivalence
  • Monotone set function
  • Semicopula
  • Universal integral

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Information Systems

Cite this

Klement, E. P., Mesiar, R., & Pap, E. (2007). A universal integral. In New Dimensions in Fuzzy Logic and Related Technologies - Proceedings of the 5th EUSFLAT 2005 Conference (Vol. 1, pp. 253-256)

A universal integral. / Klement, Erich Peter; Mesiar, Radko; Pap, E.

New Dimensions in Fuzzy Logic and Related Technologies - Proceedings of the 5th EUSFLAT 2005 Conference. Vol. 1 2007. p. 253-256.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Klement, EP, Mesiar, R & Pap, E 2007, A universal integral. in New Dimensions in Fuzzy Logic and Related Technologies - Proceedings of the 5th EUSFLAT 2005 Conference. vol. 1, pp. 253-256, 5th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2007, Ostrava, Czech Republic, 9/11/07.
Klement EP, Mesiar R, Pap E. A universal integral. In New Dimensions in Fuzzy Logic and Related Technologies - Proceedings of the 5th EUSFLAT 2005 Conference. Vol. 1. 2007. p. 253-256
Klement, Erich Peter ; Mesiar, Radko ; Pap, E. / A universal integral. New Dimensions in Fuzzy Logic and Related Technologies - Proceedings of the 5th EUSFLAT 2005 Conference. Vol. 1 2007. pp. 253-256
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