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International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems

IPMU 2012: Advances in Computational Intelligence pp 278–285Cite as

On Weak Null-Additivity of Monotone Measures

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 300))

Abstract

In this note, the relations between weak null-additivity and pseudometric generating property of monotone measures are discussed. We show that on finite continuous monotone measure spaces \((X, {\cal F}, \mu)\), if measurable space \((X, {\cal F})\) is S-compact (especially, if X is countable), then the weak null-additivity is equivalent to pseudometric generating property. We put a question: abandoning the S-compactness condition, does the equivalence remain valid?

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Author information

Authors and Affiliations

  1. School of Science, Communication University of China, Beijing, 100024, China

    Jun Li

  2. Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, SK-81368, Bratislava, Slovakia

    Radko Mesiar

  3. College of Mathematics and Informational Technology, Xinjiang Educational Institute, Urumqi, Xinjiang, 830043, China

    Hemin Wu

Authors
  1. Jun Li
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  2. Radko Mesiar
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  3. Hemin Wu
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Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco  & Benedetto Matarazzo  & 

  2. CNRS UMR 7606, DAPA, LIP6 8, Université Pierre et Marie Curie - Paris6, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute — IONA College,, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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© 2012 Springer-Verlag Berlin Heidelberg

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Li, J., Mesiar, R., Wu, H. (2012). On Weak Null-Additivity of Monotone Measures. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31724-8_29

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  • DOI: https://doi.org/10.1007/978-3-642-31724-8_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31723-1

  • Online ISBN: 978-3-642-31724-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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