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Use and Applications of Non-Additive Measures and Integrals

, 2014
Non-additive measures (also known as fuzzy measures and capacities) and integrals have been used in several types of applications. In this chapter we review the main definitions related to these measures, motivate their use from the point of view of the applications, and describe their use in different contexts. © 2014 Springer International Publishing
V. Torra
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Additive representations of non-additive measures and the choquet integral [PDF]

Annals of Operations Research, 1994
Real-valued mappings \(v\) defined on a finite algebra are considered satisfying the condition \(v(\emptyset)= 0\) (so-called non-additive measures or capacities). Various properties of the Choquet integral with respect to \(v\) are considered. Especially, a Radon-Nikodým derivative is defined and Bayesian update of a non-additive measure is derived ...
I. Gilboa, D. Schmeidler
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Entropy for non-additive measures in continuous domains

Fuzzy Sets and Systems, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
V. Torra
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On non-additive probability measures

Mathematica Slovaca, 2017
Abstract The additivity of considered measures or integrals resp. can be omitted in some problems of mathematical analysis and its applications. In the paper it is shown that similar situations are possible also in the probability theory. As an example is proved a generalized version of the central limit theorem about the convergence of
Beloslav Riečan, Karol Samuelčik
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Solving nonlinear equations by non-additive measures

Nonlinear Analysis: Theory, Methods & Applications, 1997
The paper contains a review of some nonstandard methods in measure and integration theory (nonadditive set functions, Choquet and Sugeno integral, \(\oplus\)-decomposable measures) and their applications to nonlinear partial differential equations, optimization and decision theory.
E. Pap
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Updating non-additive measures with fuzzy information

Fuzzy Sets and Systems, 1998
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V. Young, Shaun S. Wang
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On the polytope of non-additive measures

Fuzzy Sets and Systems, 2008
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E. Combarro, P. Miranda
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A Note on Extensions of Non-additive Measures

International Journal of Theoretical Physics, 2019
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Pavel Pták, Hans Weber
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EGOROFF'S THEOREM ON MONOTONE NON-ADDITIVE MEASURE SPACES

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2004
In this paper, the well-known Egoroff's theorem in classical measure theory is established on monotone non-additive measure spaces. Taylor's theorem, which concerns almost everywhere convergence of measurable function sequence in classical measure theory, is also generalized.
Li, Jun, Yasuda, Masami
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On Regularity for Non-additive Measure

2011
In this paper, we give a certain result on the regularity for nonadditive Borel measure under the conditions of weakly null additivity, a continuity from above, and a certain additional continuity.
Toshikazu Watanabe, Tamaki Tanaka
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