Decompositions and range for additive fuzzy measures

Research output: Contribution to journalArticlepeer-review


The aim of the present paper is to prove the existence of Hahn and Lebesgue decompositions for additive fuzzy measures in the sense of [3]. It is shown that the Radon-Nikodym theorem can be carried over from classical measures to additive fuzzy measures with their corresponding integrals. These results are applied to obtain a generalization of Liapounoff's convexity theorem [12] whose utility in the theory of fuzzy games is argued in the last section.

Original languageEnglish
Pages (from-to)135-155
Number of pages21
JournalFuzzy Sets and Systems
Issue number1-3
StatePublished - 1983
Externally publishedYes


  • Additive fuzzy measure
  • Darboux property of an n-vector fuzzy measure
  • Fuzzy game
  • Fuzzy game with bounded variation
  • Hahn decomposition
  • Jordan decomposition
  • Lebesgue decomposition
  • n-vector fuzzy measure
  • σ-algebra of fuzzy sets

ASJC Scopus subject areas

  • Logic
  • Artificial Intelligence


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