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An Approach to Parameterized Approximation of Crisp and Fuzzy Sets

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Rough Sets and Current Trends in Computing (RSCTC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4259))

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Abstract

This paper proposes a concept of parameterized approximation of crisp and fuzzy sets, basing on the notion of rough and fuzzy rough inclusion function. A definition of a single ε-approximation is given. It is suitable for expressing the lower and upper approximations defined in the rough set theory and the variable precision rough set model. A unified form of approximation is especially advantageous in the case of fuzzy information systems. It helps to avoid problems caused by different forms of fuzzy connectives used in the original definition of fuzzy rough sets. The presented parameterized approach to approximation constitutes an easy to implement, straightforward generalization of the variable precision crisp and fuzzy rough set model.

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Author information

Authors and Affiliations

  1. Department of Avionics and Control, Rzeszów University of Technology, ul. W. Pola 2, 35-959, Rzeszów, Poland

    Alicja Mieszkowicz-Rolka & Leszek Rolka

Authors
  1. Alicja Mieszkowicz-Rolka
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  2. Leszek Rolka
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Editor information

Editors and Affiliations

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

    Salvatore Greco

  2. Graduate School of Engineering, Department of Electrical Engineering and Computer Sciences, University of Hyogo, 2167 Shosha, 671-2280,, Himeji, Hyogo, Japan

    Yutaka Hata

  3. Department of Medical Informatics, Faculty of Medicine, Shimane University, 89-1 Enya-cho, Izumo, 693-8501, Shimane, Japan

    Shoji Hirano

  4. Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, Toyonaka, 560-8531, Osaka, Japan

    Masahiro Inuiguchi

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

    Sadaaki Miyamoto

  6. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Hung Son Nguyen

  7. Systems Research Institute, Polish Academy of Sciences, 01-447, Warsaw, Poland

    Roman Słowiński

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© 2006 Springer-Verlag Berlin Heidelberg

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Mieszkowicz-Rolka, A., Rolka, L. (2006). An Approach to Parameterized Approximation of Crisp and Fuzzy Sets. In: Greco, S., et al. Rough Sets and Current Trends in Computing. RSCTC 2006. Lecture Notes in Computer Science(), vol 4259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11908029_15

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  • DOI: https://doi.org/10.1007/11908029_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-47693-1

  • Online ISBN: 978-3-540-49842-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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