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An Interpretation of Belief Functions on Infinite Universes in the Theory of Rough Sets

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Rough Sets and Current Trends in Computing (RSCTC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5306))

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Abstract

A general type of belief structure and its inducing dual pair of belief and plausibility functions on infinite universes of discourse are first defined. Relationship between belief and plausibility functions in Dempser-Shafer theory of evidence and the lower and upper approximations in rough set theory is then established. It is shown that the probabilities of lower and upper approximations induced by an approximation space yield a dual pair of belief and plausibility functions. And for any belief structure there must exist a probability approximation space such that the belief and plausibility functions defined by the given belief structure are just respectively the lower and upper probabilities induced by the approximation space. Finally, essential properties of the belief and plausibility functions are examined. The belief and plausibility functions are respective a monotone Choquet capacity and an alternating Choquet capacity of infinite order.

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Author information

Authors and Affiliations

  1. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang, 316004, P.R. China

    Wei-Zhi Wu

  2. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei, 050016, P.R. China

    Ju-Sheng Mi

Authors
  1. Wei-Zhi Wu
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  2. Ju-Sheng Mi
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Editor information

Editors and Affiliations

  1. Department of Computer Science, The University of Akron, OH 44325-4003, Akron, USA

    Chien-Chung Chan

  2. Department of Electrical Engineering and Computer Science, University of Kansas, KS 66045, Lawrence, USA

    Jerzy W. Grzymala-Busse

  3. Department of Computer Science, University of Regina,, S4S 0A2, Regina, Saskatchewan, Canada

    Wojciech P. Ziarko

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© 2008 Springer-Verlag Berlin Heidelberg

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Wu, WZ., Mi, JS. (2008). An Interpretation of Belief Functions on Infinite Universes in the Theory of Rough Sets. In: Chan, CC., Grzymala-Busse, J.W., Ziarko, W.P. (eds) Rough Sets and Current Trends in Computing. RSCTC 2008. Lecture Notes in Computer Science(), vol 5306. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88425-5_8

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  • DOI: https://doi.org/10.1007/978-3-540-88425-5_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88423-1

  • Online ISBN: 978-3-540-88425-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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