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Measurable Structures of \({\cal I}\)-Fuzzy Rough Sets

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Book cover Rough Sets and Current Trends in Computing (RSCTC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8536))

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Abstract

In this paper, dual fuzzy rough approximation operators determined by a fuzzy implication operator \({\cal I}\) in infinite universes of discourse are first introduced. Measurable structures of \({\cal I}\)-fuzzy rough sets are then discussed. It is shown that the family of all definable sets in an \({\cal I}\)-fuzzy rough set algebra derived from a reflexive fuzzy space forms a σ-fuzzy algebra. In a finite universe of discourse, the family of all definable sets in a serial \({\cal I}\)-fuzzy rough set algebra is a fuzzy algebra, and conversely if a σ-fuzzy algebra is generated by a crisp algebra, then there must exist an \({\cal I}\)-fuzzy rough set algebra such that the family of all definable sets is exactly the given σ-fuzzy algebra.

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Authors and Affiliations

  1. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang, 316022, China

    Wei-Zhi Wu, Xiao-Feng Mu, You-Hong Xu & Xia Wang

  2. Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Wei-Zhi Wu & You-Hong Xu

Authors
  1. Wei-Zhi Wu
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  2. Xiao-Feng Mu
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  3. You-Hong Xu
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  4. Xia Wang
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Artificial Intelligence, University of Granada, Calle del Periodista Daniel Saucedo Aranda s/n, 18071, Granada, Spain

    Chris Cornelis

  2. Institute of Computer Science, Warsaw University of Technology, Nowowiejska 15/19, 00-665, Warsaw, Poland

    Marzena Kryszkiewicz

  3. University of Warsaw, Poland

    Dominik Ślȩzak

  4. Polytechnic University of Madrid, Spain

    Ernestina Menasalvas Ruiz

  5. Deparment of Computer Sciences, Universidad Central Marta Abreu de las Villas, Santa Clara, Villa Clara, Cuba

    Rafael Bello

  6. Department of Computer Science and Technology, Nanjing University, 210023, Nanjing, China

    Lin Shang

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© 2014 Springer International Publishing Switzerland

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Wu, WZ., Mu, XF., Xu, YH., Wang, X. (2014). Measurable Structures of \({\cal I}\)-Fuzzy Rough Sets. In: Cornelis, C., Kryszkiewicz, M., Ślȩzak, D., Ruiz, E.M., Bello, R., Shang, L. (eds) Rough Sets and Current Trends in Computing. RSCTC 2014. Lecture Notes in Computer Science(), vol 8536. Springer, Cham. https://doi.org/10.1007/978-3-319-08644-6_9

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  • DOI: https://doi.org/10.1007/978-3-319-08644-6_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08643-9

  • Online ISBN: 978-3-319-08644-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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