Abstract
There are two generalizations for k-additive set functions: constructive k-additivity and formulaic k-additivity. We study some properties around these concepts and their relations. A constructively k-additive set function is always formulaic k-additive. For a distorted measure, these two concepts are equivalent. Under certain conditions of “bounded variation” and “continuity at the \(\emptyset \),” we prove the constructive k-additivity for a formulaic k-additive set function.
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Fukuda, R., Honda, A., Okazaki, Y. (2021). On Two Generalizations for k-Additivity. In: Torra, V., Narukawa, Y. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2021. Lecture Notes in Computer Science(), vol 12898. Springer, Cham. https://doi.org/10.1007/978-3-030-85529-1_4
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DOI: https://doi.org/10.1007/978-3-030-85529-1_4
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