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Regularity Properties of Null-Additive Fuzzy Measure on Metric Spaces

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Modeling Decisions for Artificial Intelligence (MDAI 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3558))

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Abstract

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.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, College of Science, Communication University of China, Beijing, 100024, China

    Jun Li

  2. Dep of Math & Infor, Chiba University, Chiba, 263-8522, Japan

    Masami Yasuda

  3. Department of Computer Science and Engineering, Tianjin University of Technology, Tianjin, 300191, China

    Jinjie Song

Authors
  1. Jun Li
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  2. Masami Yasuda
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  3. Jinjie Song
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Editor information

Editors and Affiliations

  1. IIIA, Artificial Intelligence Research Institute CSIC, Spanish National Research Council, Campus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

  2. Toho Gakuen, 3-1-10 Naka, Kunitachi, 186-0004, Tokyo, Japan

    Yasuo Narukawa

  3. Department of Risk Engineering, School of Systems and Information Engineering, University of Tsukuba, 305-8573, Ibaraki, Japan

    Sadaaki Miyamoto

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© 2005 Springer-Verlag Berlin Heidelberg

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Li, J., Yasuda, M., Song, J. (2005). Regularity Properties of Null-Additive Fuzzy Measure on Metric Spaces. In: Torra, V., Narukawa, Y., Miyamoto, S. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2005. Lecture Notes in Computer Science(), vol 3558. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11526018_7

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  • DOI: https://doi.org/10.1007/11526018_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27871-9

  • Online ISBN: 978-3-540-31883-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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