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Simple Undirected Graphs as Formal Contexts

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Formal Concept Analysis (ICFCA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9113))

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Abstract

The adjacency matrix of a graph is interpreted as a formal context. Then, the counterpart of Formal Concept Analysis (FCA) tools are introduced in graph theory. Moreover, a formal context is seen as a Boolean information table, the structure at the basis of Rough Set Theory (RST). Hence, we also apply RST tools to graphs. The peculiarity of the graph case, put in evidence and studied in the paper, is that both FCA and RST are based on a (different) binary relation between objects.

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References

  1. Alexe, G., Alexe, S., Crama, Y., Foldes, S., Hammer, P.L., Simeone, B.: Consensus algorithms for the generation of all maximal bicliques. Discrete Appl. Math. 145, 11–21 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ciucci, D., Dubois, D., Prade, H.: The structure of oppositions in rough set theory and formal concept analysis - toward a new bridge between the two settings. In: Beierle, C., Meghini, C. (eds.) FoIKS 2014. LNCS, vol. 8367, pp. 154–173. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  3. Dawande, M., Keskinocak, P., Swaminathan, J.M., Tayur, S.: On bipartite and multipartite clique problems. J. Algorithms 41, 388–403 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dubois, D., Dupin de Saint Cyr, F., Prade, H.: A possibility-theoretic view of formal concept analysis. Fundamenta Informaticae 75, 195–213 (2007)

    MATH  MathSciNet  Google Scholar 

  5. Dubois, D., Prade, H.: From Blanché’s hexagonal organization of concepts to formal concept analysis and possibility theory. Log. Univers. 6, 149–169 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)

    Book  MATH  Google Scholar 

  7. Gaume, B., Navarro, E., Prade, H.: A parallel between extended formal concept analysis and bipartite graphs analysis. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS, vol. 6178, pp. 270–280. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  8. Kuznetsov, S.O., Obiedkov, S.A.: Comparing performance of algorithms for generating concept lattices. J. Exp. Theor. Artif. Intell. 14, 189–216 (2002)

    Article  MATH  Google Scholar 

  9. Li, J., Liu, G., Li, H., Wong, L.: Maximal biclique subgraphs and closed pattern pairs of the adjacency matrix: a one-to-one correspondence and mining algorithms. IEEE Trans. Knowl. Data Eng. 19, 1625–1637 (2007)

    Article  Google Scholar 

  10. Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Publisher, The Netherlands (1991)

    Book  MATH  Google Scholar 

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Correspondence to Davide Ciucci .

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Chiaselotti, G., Ciucci, D., Gentile, T. (2015). Simple Undirected Graphs as Formal Contexts. In: Baixeries, J., Sacarea, C., Ojeda-Aciego, M. (eds) Formal Concept Analysis. ICFCA 2015. Lecture Notes in Computer Science(), vol 9113. Springer, Cham. https://doi.org/10.1007/978-3-319-19545-2_18

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  • DOI: https://doi.org/10.1007/978-3-319-19545-2_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19544-5

  • Online ISBN: 978-3-319-19545-2

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