Integrals based on monotone set functions

Erich Peter Klement, Jun Li, Radko Mesiar, E. Pap

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

An overview of various integrals is given which can be defined on arbitrary monotone set functions vanishing in the empty set (called here monotone measures). Our survey includes not only the Choquet integral (1954) [10], the Shilkret integral (1971) [66] and the Sugeno integral (1974) [71] and some of their properties, but also some more general and more recent concepts as universal integrals Klement et al. (2010) [27] and decomposition integrals Even (2014) [13], together with some of their properties, such as integral inequalities and convergence theorems.

Original languageEnglish
Pages (from-to)88-102
Number of pages15
JournalFuzzy Sets and Systems
Volume281
DOIs
Publication statusPublished - Dec 15 2015

Fingerprint

Monotone
Decomposition
Sugeno Integral
Choquet Integral
Null set or empty set
Integral Inequality
Convergence Theorem
Decompose
Arbitrary

Keywords

  • Choquet integral
  • Decomposition integral
  • Monotone measure
  • Shilkret integral
  • Sugeno integral
  • Universal integral

ASJC Scopus subject areas

  • Artificial Intelligence
  • Logic

Cite this

Integrals based on monotone set functions. / Klement, Erich Peter; Li, Jun; Mesiar, Radko; Pap, E.

In: Fuzzy Sets and Systems, Vol. 281, 15.12.2015, p. 88-102.

Research output: Contribution to journalArticle

Klement, Erich Peter ; Li, Jun ; Mesiar, Radko ; Pap, E. / Integrals based on monotone set functions. In: Fuzzy Sets and Systems. 2015 ; Vol. 281. pp. 88-102.
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