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On the f-divergence for discrete non-additive measures

Information Sciences, 2020
Distances 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, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pavel Pták, Hans Weber
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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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Non-additive measures by interval probability functions

Information Sciences, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hideo Tanaka   +2 more
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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
Beloslav Riečan, Karol Samuelčik
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On Lusin’s Theorem for Non-additive Measure

2011
In 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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Updating non-additive measures with fuzzy information

Fuzzy Sets and Systems, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Virginia R. Young, Shaun S. Wang
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Conditioning (updating) non-additive measures

Annals of Operations Research, 1994
Several 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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Lebesgue theorems in non-additive measure theory

Fuzzy Sets and Systems, 2005
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Jinjie Song, Jun Li
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Some aspects of non-additive measures

2015 IEEE 13th International Symposium on Intelligent Systems and Informatics (SISY), 2015
It is a well known fact that non-additive measures, i.e., monotone set functions, and corresponding integrals have been successfully applied in many different areas, both theoretical and practical. Due to the course of research, this problem has diversified into two directions.
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