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Radon-Nikodym Theorem for Fuzzy Set-Valued Measures*

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Book cover Fuzzy Sets Theory and Applications

Part of the book series: NATO ASI Series ((ASIC,volume 177))

Abstract

We study fuzzy set-valued measures in a Banach space and their relationships with fuzzy random variables. This theory is motivated by the need for a rigorous framework for the problem of inexact measurement. Our main result is a theorem of the Radon-Nikodym type for a fuzzy measure which is absolutely continuous with respect to a probability measure. Our result extends corresponding results for vector measures and for set-valued measures.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Cincinnati, 45221, Ohio, USA

    D. A. Ralescu

Authors
  1. D. A. Ralescu
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Editor information

Editors and Affiliations

  1. Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    André Jones

  2. O.R. and M.S Consultant, Grenoble, France

    Arnold Kaufmann

  3. Institute of Technology, Aachen, Germany

    Hans-Jürgen Zimmermann

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© 1986 D. Reidel Publishing Company

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Ralescu, D.A. (1986). Radon-Nikodym Theorem for Fuzzy Set-Valued Measures*. In: Jones, A., Kaufmann, A., Zimmermann, HJ. (eds) Fuzzy Sets Theory and Applications. NATO ASI Series, vol 177. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4682-8_2

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  • DOI: https://doi.org/10.1007/978-94-009-4682-8_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8581-6

  • Online ISBN: 978-94-009-4682-8

  • eBook Packages: Springer Book Archive

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