Some properties of the variations of non-additive set functions. I

DOI10.1016/S0165-0114(98)00422-9zbMath0973.28015OpenAlexW4245293706MaRDI QIDQ5931171

Qiang Zhang

Publication date: 6 May 2001

Published in: Fuzzy Sets and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0165-0114(98)00422-9

zbMATH Keywords

fuzzy measureschain variationdecomposition of signed measuresdisjoint variationexhaustivitynon-additive set functionsnull-additivityorder continuity

Mathematics Subject Classification ID

Fuzzy measure theory (28E10)

Related Items (7)

Pseudo-atoms, atoms and a Jordan type decomposition in effect algebras ⋮ Choquet type \(L^{1}\)-spaces of a vector capacity ⋮ Some new results on Dieudonné-type theorems for \(k\)-triangular lattice group-valued set functions ⋮ Some properties of the variations of non-additive set functions on \(T\)-tribes ⋮ Some properties of the variations of non-additive set functions. II ⋮ Functions of bounded variation on effect algebras ⋮ Variations on effect algebras.

Cites Work

• The autocontinuity of set function and the fuzzy integral
• On fuzzy measures defined by fuzzy integrals
• The fuzzy integral
• On the null-additivity and the autocontinuity of a fuzzy measure
• Lebesgue decomposition theorem for \(\sigma\)-finite signed fuzzy measures
• Further discussion on the Hahn decomposition theorem for signed fuzzy measure
• Non-monotonic fuzzy measures and the Choquet integral
• Lebesgue and Saks decompositions of \(\sigma\)-finite fuzzy measures
• Values of Non-Atomic Games
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