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On the f -divergence for non-additive measures
Fuzzy Sets and Systems, 2016The f-divergence evaluates the dissimilarity between two probability distributions defined in terms of the Radon-Nikodym derivative of these two probabilities. The f-divergence generalizes the Hellinger distance and the Kullback-Leibler divergence among other divergence functions. In this paper we define an analogous function for non-additive measures.
Vicenç Torra +2 more
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On the f-divergence for discrete non-additive measures
Information Sciences, 2020Distances of probability measures, including f-divergences, Hellinger distance, Kullback-Leibler divergence, etc., play an important role in information theory and statistics. In several cases, the connection between these distances and Radon-Nikodym derivatives is exploited.
Vicenç Torra +2 more
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A Note on Extensions of Non-additive Measures
International Journal of Theoretical Physics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pavel Pták, Hans Weber
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On Regularity for Non-additive Measure
2011In 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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Non-additive measures by interval probability functions
Information Sciences, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hideo Tanaka +2 more
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On non-additive probability measures
Mathematica Slovaca, 2017Abstract 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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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 ...
Itzhak Gilboa, David Schmeidler
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Conditioning (updating) non-additive measures
Annals of Operations Research, 1994Several update rules for non-additive probabilities, among them the Dempster-Shafer rule for belief functions and certain update rules in the spirit of Bayesian statistics with multiple prior probabilities, are reviewed, investigated and compared with each other. This is done within the unifying framework of general, nonadditive measure and integration
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On Lusin’s Theorem for Non-additive Measure
2011In this paper, we prove Lusin’s theorem remains valid for nonadditive Borel measure under the conditions of weakly null additivity, continuity from above and a certain additional continuity.
Tamaki Tanaka, Toshikazu Watanabe
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On the Visualization of Discrete Non-additive Measures
2017Non-additive measures generalize additive measures, and have been utilized in several applications. They are used to represent different types of uncertainty and also to represent importance in data aggregation. As non-additive measures are set functions, the number of values to be considered grows exponentially.
Juhee Bae +3 more
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