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Direct Factorization by Similarity of Fuzzy Concept Lattices by Factorization of Input Data

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Concept Lattices and Their Applications (CLA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4923))

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Abstract

The paper presents additional results on factorization by similarity of fuzzy concept lattices. A fuzzy concept lattice is a hierarchically ordered collection of clusters extracted from tabular data. The basic idea of factorization by similarity is to have, instead of a possibly large original fuzzy concept lattice, its factor lattice. The factor lattice contains less clusters than the original concept lattice but, at the same time, represents a reasonable approximation of the original concept lattice and provides us with a granular view on the original concept lattice. The factor lattice results by factorization of the original fuzzy concept lattice by a similarity relation. The similarity relation is specified by a user by means of a single parameter, called a similarity threshold. Smaller similarity thresholds lead to smaller factor lattices, i.e. to more comprehensible but less accurate approximations of the original concept lattice. Therefore, factorization by similarity provides a trade-off between comprehensibility and precision. We first recall the notion of factorization. Second, we present a way to compute the factor lattice of a fuzzy concept lattice directly from input data, i.e. without the need to compute the possibly large original concept lattice.

Supported by grant No. 1ET101370417 of GA AV ČR, by grant No. 201/05/0079 of the Czech Science Foundation, and by institutional support, research plan MSM 6198959214.

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Authors and Affiliations

  1. Dept. Systems Science and Industrial Engineering T. J. Watson School of Engineering and Applied Science, Binghamton University–SUNY, PO Box 6000, Binghamton, NY 13902–6000, USA

    Radim Belohlavek & Vilem Vychodil

  2. Dept. Computer Science, Palacky University, Olomouc Tomkova 40, CZ-779 00, Olomouc, Czech Republic

    Radim Belohlavek, Jan Outrata & Vilem Vychodil

Authors
  1. Radim Belohlavek
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  2. Jan Outrata
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  3. Vilem Vychodil
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Editor information

Sadok Ben Yahia Engelbert Mephu Nguifo Radim Belohlavek

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Belohlavek, R., Outrata, J., Vychodil, V. (2008). Direct Factorization by Similarity of Fuzzy Concept Lattices by Factorization of Input Data. In: Yahia, S.B., Nguifo, E.M., Belohlavek, R. (eds) Concept Lattices and Their Applications. CLA 2006. Lecture Notes in Computer Science(), vol 4923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78921-5_4

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  • DOI: https://doi.org/10.1007/978-3-540-78921-5_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78920-8

  • Online ISBN: 978-3-540-78921-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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