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The Total Variation Distance for Comparing Non-Additive Measures.

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Názov: The Total Variation Distance for Comparing Non-Additive Measures.
Autori: Nieto-Barba, David1 (AUTHOR) nietodavid@uniovi.es, Miranda, Enrique1 (AUTHOR) mirandaenrique@uniovi.es, Montes, Ignacio1 (AUTHOR) imontes@uniovi.es
Zdroj: International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems. Oct2025, Vol. 33 Issue 7, p827-853. 27p.
Predmety: *DISTRIBUTION (Probability theory), *MATHEMATICAL analysis, COOPERATIVE game theory, CONVEX sets, FUZZY measure theory, STATISTICAL measurement, STATISTICAL bias
Abstrakt: The Total Variation is a common distance between probability distributions that measures the maximum difference in probability among all events. When comparing non-additive measures, that can be represented by closed and convex sets of probability measures, the Total Variation distance can be extended in multiple ways. This paper explores three specific approaches in detail. The first approach considers the minimum Total Variation distance between the probability measures dominating the non-additive measures. The second approach replaces the minimum with the maximum of the Total Variation distances. The third approach modifies the first one by using the supremum distance instead of the Total Variation. We analyse the main properties of each approach and, in particular, apply them to distort non-additive measures. Finally, we demonstrate that the distortion of non-additive measures with the proposed extensions are closely connected to the strong and weak cores in coalition game theory. [ABSTRACT FROM AUTHOR]
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Abstrakt:The Total Variation is a common distance between probability distributions that measures the maximum difference in probability among all events. When comparing non-additive measures, that can be represented by closed and convex sets of probability measures, the Total Variation distance can be extended in multiple ways. This paper explores three specific approaches in detail. The first approach considers the minimum Total Variation distance between the probability measures dominating the non-additive measures. The second approach replaces the minimum with the maximum of the Total Variation distances. The third approach modifies the first one by using the supremum distance instead of the Total Variation. We analyse the main properties of each approach and, in particular, apply them to distort non-additive measures. Finally, we demonstrate that the distortion of non-additive measures with the proposed extensions are closely connected to the strong and weak cores in coalition game theory. [ABSTRACT FROM AUTHOR]
ISSN:02184885
DOI:10.1142/S0218488525400112