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Necessary and sufficient conditions in terms of Mobius transform for $k$-monotonicity of set functions (Information and mathematics of non-additivity and non-extensivity : non-additivity and convex analysis)

Necessary and sufficient conditions in terms of Mobius transform for $k$-monotonicity of set functions (Information and mathematics of non-additivity and non-extensivity : non-additivity and convex analysis)
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Extensions of (weakly) null-additive, monotone set functions from rings to generated algebras(Information and mathematics of non-additivity and non-extensivity : from the viewpoint of functional analysis)

Extensions of (weakly) null-additive, monotone set functions from rings to generated algebras(Information and mathematics of non-additivity and non-extensivity : from the viewpoint of functional analysis)
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Additive indecomposability of submodular set functions and its generalization (Information and mathematics of non-additivity and non-extensivity : contacts with nonlinearity and non-commutativity)

Additive indecomposability of submodular set functions and its generalization (Information and mathematics of non-additivity and non-extensivity : contacts with nonlinearity and non-commutativity)
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Interactions with polygenic background impact quantitative traits in the UK Biobank

Ferreira LAF, Hu S, Davies RW, Myers SR.
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Linear non-additive set-functions

International Journal of General Systems, 2004
It is known that for basic linear fuzzy measures the Aumann and the Choquet integrals defined on a special class of fuzzy subsets of some Banach space commute. We characterize basic linear fuzzy measures by means of appropriate linear functionals, and consequently the relevant integral representation (by means of the Lebesgue integral) is introduced ...
Bouchon-Meunier, Bernadette, Mesiar, Radko, Ralescu, Dan A.   +2 more
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Darboux property of a non-additive set function

Sbornik: Mathematics, 2001
It is known that the range of a non-atomic measure on a \(\sigma\)-algebra is a closed interval. The authors generalize that result to the case of non-additive set functions defined on an F-algebra and satisfying the Saks decomposition property instead on non-atomicity (an algebra \(\Sigma\) of sets is an F algebra if for each increasing sequence ...
Klimkin, V. M., Svistula, M. G.
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The inclusion variation of non-additive set functions

Ninth IEEE International Conference on Fuzzy Systems. FUZZ- IEEE 2000 (Cat. No.00CH37063), 2002
We continue the work of a paper by Zhang to introduce the concepts of a third kind of variations for non-additive set functions, the inclusion variations, and discuss some properties of the variations. In particular, we investigate the inclusion variations of signed fuzzy measures, which are closely linked to the uniqueness of Jordan decomposition of ...
null Qiang Zhang, null Ziyou Gao
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The chain variation of non-additive set functions

FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315), 1999
We discuss some properties of the chain variations for non-additive set functions, such as the null-additivity, exhaustivity, order continuity and continuity. The Jordan decomposition theorem is also presented and proved for signed lower semicontinuous fuzzy measures.
null Qiang Zhang, null Baoding Liu, null Guozhong Ma   +2 more
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Some properties of the variations of non-additive set functions II

Fuzzy Sets and Systems, 2001
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Zhang, Qiang, Gao, Ziyou
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