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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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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 ...
Qiang Zhang, Ziyou Gao
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Some properties of the variations of non-additive set functions II

Fuzzy Sets and Systems, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qiang Zhang, 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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The Inclusion Variation of Non-additive Set Functions on T-Tribe

Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007), 2007
Inclusion variation on Tinfin-tribe play an important role in Tinfin-measures and fuzzy games theory, where they were used for additive set functions on Tinfin-tribe. In this paper classical variations theory is extended to non-additive set functions on T-tribe, after defining the inclusion variation, we investigate its some properties in detailed ...
Chunqiao Tan, Qiang Zhang 0010, Wangbin Hu   +2 more
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Some properties of the variations of non-additive set functions on T-tribes

Fuzzy Sets and Systems, 2007
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Chunqiao Tan, Qiang Zhang 0010
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Regularity properties of non-additive set functions

Fuzzy Sets and Systems, 1991
A variant of the Lebesgue decomposition theorem is proved for so-called decomposable measures with regard to a triangular conorm. A similar result (of course, not including the result mentioned above) has been achieved by \textit{E. Pap} [Fuzzy Sets Syst. 38, No. 3, 345-353 (1990; Zbl 0722.28015)].
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