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Lindig’s Algorithm for Concept Lattices over Graded Attributes

  • Conference paper
Modeling Decisions for Artificial Intelligence (MDAI 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4617))

Abstract

Formal concept analysis (FCA) is a method of exploratory data analysis. The data is in the form of a table describing relationship between objects (rows) and attributes (columns), where table entries are grades representing degrees to which objects have attributes. The main output of FCA is a hierarchical structure (so-called concept lattice) of conceptual clusters (so-called formal concepts) present in the data. This paper focuses on algorithmic aspects of FCA of data with graded attributes. Namely, we focus on the problem of generating efficiently all clusters present in the data together with their subconcept-superconcept hierarchy. We present theoretical foundations, the algorithm, analysis of its efficiency, and comparison with other algorithms.

Supported by Kontakt 1–2006–33 (Bilateral Scientific Cooperation, project “Algebraic, logical and computational aspects of fuzzy relational modelling paradigms”), 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

  2. Dept. Appl. Math., Biometrics, and Process Control, Ghent University, Coupure links 653, B-9000 Gent, Belgium

    Bernard De Baets

  3. 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. Bernard De Baets
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  3. Jan Outrata
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  4. Vilem Vychodil
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Vicenç Torra Yasuo Narukawa Yuji Yoshida

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Belohlavek, R., De Baets, B., Outrata, J., Vychodil, V. (2007). Lindig’s Algorithm for Concept Lattices over Graded Attributes. In: Torra, V., Narukawa, Y., Yoshida, Y. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2007. Lecture Notes in Computer Science(), vol 4617. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73729-2_15

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  • DOI: https://doi.org/10.1007/978-3-540-73729-2_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73728-5

  • Online ISBN: 978-3-540-73729-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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