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Abstract
Concept lattices are systems of conceptual clusters, called formal concepts, which are partially ordered by the sub concept/superconcept relationship. Concept lattices are basic structures used in formal concept analysis. In general, a concept lattice may contain overlapping clusters and need not be a tree. On the other hand, tree-like classification schemes are appealing and are produced by several clustering methods. In this paper, we present necessary and sufficient conditions on input data for the output concept lattice to form a tree after one removes its least element. We present these conditions for input data with yes/no attributes as well as for input data with fuzzy attributes. In addition, we show how Lindig's algorithm for computing concept lattices gets simplified when applied to input data for which the associated concept lattice is a tree after removing the least element. The paper also contains illustrative examples.
Keywords
FORMAL CONCEPT ANALYSIS, formal concept, attribute implication, tree, concept lattice

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Citation

Please use this url to cite or link to this publication:

MLA
Belohlavek, Radim et al. “Characterizing Trees in Concept Lattices.” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 16.1 (2008): 1–15. Print.
APA
Belohlavek, R., De Baets, B., Outrata, J., & Vychodil, V. (2008). Characterizing trees in concept lattices. INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 16(1), 1–15.
Chicago author-date
Belohlavek, Radim, Bernard De Baets, Jan Outrata, and Vilem Vychodil. 2008. “Characterizing Trees in Concept Lattices.” International Journal of Uncertainty Fuzziness and Knowledge-based Systems 16 (1): 1–15.
Chicago author-date (all authors)
Belohlavek, Radim, Bernard De Baets, Jan Outrata, and Vilem Vychodil. 2008. “Characterizing Trees in Concept Lattices.” International Journal of Uncertainty Fuzziness and Knowledge-based Systems 16 (1): 1–15.
Vancouver
1.
Belohlavek R, De Baets B, Outrata J, Vychodil V. Characterizing trees in concept lattices. INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS. Singapore: World Scientific; 2008;16(1):1–15.
IEEE
[1]
R. Belohlavek, B. De Baets, J. Outrata, and V. Vychodil, “Characterizing trees in concept lattices,” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, vol. 16, no. 1, pp. 1–15, 2008.
@article{692639,
  abstract     = {Concept lattices are systems of conceptual clusters, called formal concepts, which are partially ordered by the sub concept/superconcept relationship. Concept lattices are basic structures used in formal concept analysis. In general, a concept lattice may contain overlapping clusters and need not be a tree. On the other hand, tree-like classification schemes are appealing and are produced by several clustering methods. In this paper, we present necessary and sufficient conditions on input data for the output concept lattice to form a tree after one removes its least element. We present these conditions for input data with yes/no attributes as well as for input data with fuzzy attributes. In addition, we show how Lindig's algorithm for computing concept lattices gets simplified when applied to input data for which the associated concept lattice is a tree after removing the least element. The paper also contains illustrative examples.},
  author       = {Belohlavek, Radim and De Baets, Bernard and Outrata, Jan and Vychodil, Vilem},
  issn         = {0218-4885},
  journal      = {INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS},
  keywords     = {FORMAL CONCEPT ANALYSIS,formal concept,attribute implication,tree,concept lattice},
  language     = {eng},
  number       = {1},
  pages        = {1--15},
  publisher    = {World Scientific},
  title        = {Characterizing trees in concept lattices},
  url          = {http://dx.doi.org/10.1142/S0218488508005212},
  volume       = {16},
  year         = {2008},
}

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