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Regularity properties of null-additive fuzzy measure on metric spaces. (English) Zbl 1121.28305
Torra, Vicenç (ed.) et al., Modeling decisions for artificial intelligence. Second international conference, MDAI 2005, Tsukuba, Japan, July 25--27, 2005. Proceedings. Berlin: Springer (ISBN 3-540-27871-0/pbk). Lecture Notes in Computer Science 3558. Lecture Notes in Artificial Intelligence, 59-66 (2005).
Summary: We shall discuss further regularity properties of null-additive fuzzy measure on metric spaces following the previous results. Under the null-additivity condition, some properties of the inner/outer regularity and the regularity of fuzzy measure are shown. Also the strong regularity of fuzzy measure is discussed on complete separable metric spaces. As an application of strong regularity, we present a characterization of atom of null-additive fuzzy measure. For the entire collection see [Zbl 1076.68011].

28E10Fuzzy measure theory
54E35Metric spaces, metrizability