Representing a Concept Lattice by Neighborly Ideas

Mao, Hua

doi:10.2478/v10324-012-0006-3

Abstract

Concept lattices are an ordering of the maximal rectangles defined by a binary relation. This paper, using the idea of neighbor sets in graph theory, presents an approach to obtain all the concepts for a context, and simultaneously gets the diagram of the concept lattice.

References

[1] J. Abello, A. J. Pogel, and L. Miller, Breadth first search graph partitions and concept lattices, J. of Universal Computer Science, 10(8), (2004), 934-954.
Search in Google Scholar
[2] A. Berry, J. Bordat, and A. Sigayret, A local approach to concept generation, Annals of Mathematics and Articial Intelligence, 49(1-4), (2007), 117-136.10.1007/s10472-007-9063-4
Search in Google Scholar
[3] A. Berry and A. Sigayret, Representing a concept lattice by a graph., Dis. Appl.Math., 144, (27-42.)10.1016/j.dam.2004.02.016
Search in Google Scholar
[4] G. Birkho, Lattice Theory. 3rd. ed. Providence, American Mathematical Society, 1967.
Search in Google Scholar
[5] J. A. Bondy, Graph Theory with Applications, Elsevier Science Publishing Co. Inc., New York, 1976.10.1007/978-1-349-03521-2
Search in Google Scholar
[6] B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, 2nd. ed. Cambridge, Cambridge University Press, 2003.
Search in Google Scholar
[7] B. Ganter and R. Wille, Formal Concept Analysis, Mathematical Foundations Heidelberg, Springer-Verlag Berlin, 1999.10.1007/978-3-642-59830-2
Search in Google Scholar
[8] G. Grätzer, General Lattice Theory. 2nd. ed. Basel, Birkhäuser Verlag, 1998.
Search in Google Scholar
[9] H. Mao, Concept lattices and co-covering graphs., Inter. J. of Alge., 3(3), (2009), 137-148.
Search in Google Scholar
[10] S. Owais, P. Gajdoš, and V. Snášel, Usage of genetic algorithm for lattice drawing, In: CLA 2005(Eds.: R. Bělohlǎvek and V. Snášel) 82-91. ISBN 80-248-0863-3.
Search in Google Scholar

Representing a Concept Lattice by Neighborly Ideas

Abstract

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