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Simple Proof of Basic Theorem for General Concept Lattices by Cartesian Representation

  • Conference paper
Book cover Modeling Decisions for Artificial Intelligence (MDAI 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7647))

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Abstract

We promote a useful representation of fuzzy sets by ordinary sets, called the Cartesian representation. In particular, we show how the main structures related to a general type of concept lattices may be reduced using this representation to their ordinary counterparts. As a consequence of this representation, we obtain a simple proof of the basic theorem for this type of concept lattices.

We acknowledge support by the Grant No. P202/10/0262 of the Czech Science Foundation (Belohlavek, Konecny, Osicka) and by IGA of Palacky University, No. PrF_20124029 (Konecny, Osicka).

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Authors and Affiliations

  1. DAMOL (Data Analysis and Modeling Laboratory) Department of Computer Science, Palacký University, Olomouc, Czech Republic

    Radim Belohlavek, Jan Konecny & Petr Osicka

Authors
  1. Radim Belohlavek
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  2. Jan Konecny
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  3. Petr Osicka
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Editor information

Editors and Affiliations

  1. IIIA-CSIC, Campus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

  2. Toho Gakuen, 3-1-10, Naka, 186-0004, Kunitachi, Tokyo, Japan

    Yasuo Narukawa

  3. Universitat de Girona, Campus Montilivi, building EPS-4, 17071, Girona, Spain

    Beatriz López  & Mateu Villaret  & 

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Belohlavek, R., Konecny, J., Osicka, P. (2012). Simple Proof of Basic Theorem for General Concept Lattices by Cartesian Representation. In: Torra, V., Narukawa, Y., López, B., Villaret, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2012. Lecture Notes in Computer Science(), vol 7647. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34620-0_27

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  • DOI: https://doi.org/10.1007/978-3-642-34620-0_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34619-4

  • Online ISBN: 978-3-642-34620-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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