Integrals based on monotone set functions

Erich Peter Klement, Jun Li, Radko Mesiar, Endre Pap

Research output: Contribution to journalArticle

38 Citations (Scopus)


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
Publication statusPublished - Dec 15 2015


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

ASJC Scopus subject areas

  • Logic
  • Artificial Intelligence

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