Atoms of weakly null-additive monotone measures and integrals

Jun Li, Radko Mesiar, Endre Pap

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

In this paper, we prove some properties of atoms of weakly null-additive monotone measures. By using the regularity and weak null-additivity, a sin-gleton characterization of atoms of monotone measures on a metric space is shown. It is a generalization of previous results obtained by Pap. The calculation of the Sugeno integral and the Choquet integral over an atom is also presented, respectively. Similar results for recently introduced universal integral are also given. Following these results, it is shown that the Sugeno integral and the Choquet integral over an atom of monotone measure is maxitive linear and standard linear, respectively. Convergence theorems for the Sugeno integral and the Choquet integral over an atom of a monotone measure are also shown.

Original languageEnglish
Pages (from-to)183-192
Number of pages10
JournalInformation Sciences
Volume257
DOIs
Publication statusPublished - Feb 1 2014

Keywords

  • Atom
  • Choquet integral
  • Monotone measure
  • Regularity
  • Sugeno integral
  • Weak null-additivity

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Theoretical Computer Science
  • Computer Science Applications
  • Information Systems and Management
  • Artificial Intelligence

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